Astronomy 112 Laboratory Manual Spring 2004 Edition

Transcript

ASTRONOMY 112 LABORATORY MANUAL DR. TSUNEFUMI TANAKA PHYSICS DEPARTMENT CALIFORNIA POLYTECHNIC STATE UNIVERSITY DR. BRETT TAYLOR DEPARTMENT OF CHEMISTRY AND PHYSICS RADFORD UNIVERSITY SPRING 2004 EDITION Contents A In-Class Activities A.1 Celestial Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Angular Resolution: Seeing Details with the Eye . . . . . . . . . . . . . . . . . . . . . . . . . A.3 Estimating the Diameter of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 11 15 B Laboratory Experiments B.1 Optics and Spectroscopy . . . B.2 Magnets: Magnetic Force and B.3 Brightness and Distance . . . B.4 How Many 200W Light Bulbs . . . . . . . . . . . . . Magnetic Field . . . . . . . . . . . . . . . . . Does It Take to Equal C Computer Laboratories (CLEA) C.1 The Classification of Stellar Spectra . . . C.2 Photoelectric Photometry of the Pleiades C.3 The Hubble Redshift-Distance Relation . C.4 The Period of Rotation of the Sun . . . . C.5 Radio Astronomy of Pulsars . . . . . . . . . . . . . . . . . . D Observations D.1 Measuring Angles in the Sky . . . . . . . . . D.2 Moon Observation . . . . . . . . . . . . . . . D.3 Constellation Quiz: Get To Know Your Night D.4 Sunspot and Prominence Observation . . . . D.5 Observation With A Telescope . . . . . . . . D.6 Moon Journal . . . . . . . . . . . . . . . . . . D.7 Observation of a Planet . . . . . . . . . . . . D.8 Observation of Deep Sky Objects . . . . . . . D.9 The Sun and Its Shadow . . . . . . . . . . . . D.10 Object X . . . . . . . . . . . . . . . . . . . . iii . . . . . . the . . . . . . . . . . . . Sun? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 21 27 33 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 49 55 61 67 71 . . . . . . Sky! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 79 87 89 91 97 103 107 109 113 117 . . . . . . . . . . Chapter A In-Class Activities 1 2 CHAPTER A. IN-CLASS ACTIVITIES CHAPTER A. IN-CLASS ACTIVITIES 3 Name: A.1 I. Section: Date: Celestial Coordinates Introduction How do you pinpoint the position of your house on the Earth? You can specify the street address or give a pair of coordinates. You can divide the surface of the Earth into grids in the east-west direction and the north-south direction. By measuring coordinates (i.e., distances or angles) from some reference points, you tell the exact position of your house. For example, the City of Radford is located at the longitude 88.6◦ west and the latitude 37.1◦ north. In this case the reference points are the meridian through Greenwich, England and the equator. In astronomy we are interested in specifying the positions of objects in the sky as seen by an observer on the Earth. It could be accomplished by giving a pair of coordinates. It helps to picture the night sky as an immense glass sphere with the Earth (and the observer) at its center and all of the stars and planets projected on the sphere (see Fig. A.1). This sphere is known as the celestial sphere. ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ Observer Horizon Figure A.1: The observable half of the celestial sphere above the horizon. There are various ways to define coordinates on the celestial sphere. In this lab we are going to study two such systems: alt-azimuth system and the equatorial system. II. Reference • 21st Century Astronomy, Appendix 6, p. A-17 – A-19 III. Materials Used • Celestial globe 4 IV. CHAPTER A. IN-CLASS ACTIVITIES Activity The Alt-Azimuth System Let us define some terminology. Suppose the observer is located at the center of the celestial sphere in Fig. A.2. The point directly overhead on the celestial sphere is called the zenith, while the point directly opposite of the zenith is the nadir. The horizon is the circle extending around the celestial sphere and located exactly 90◦ from the zenith and the nadir. Zenith Local Celestial Meridian N W Observer S E Horizon Nadir Figure A.2: The Celestial sphere. The north point (N) is located on the horizon in the direction of geographic north as seen by the observer at the center. The east (E), south (S), and west (W) points are also located along the horizon at 90◦ intervals. The local celestial meridian is the imaginary circle on the celestial sphere that runs from the north point, through the zenith, to the south point and through the nadir back to the north point. Now let us consider a star on the celestial sphere (see Fig. A.3). The circular arc running from the zenith through the star to the horizon at H is a vertical circle. The azimuth of the star is the angle along the horizon from the north point eastward to H. This is basically the compass direction (SSW for example), but measured in degrees. The altitude of the star is the angle of the star above the horizon along the vertical circle. The altitude is a positive number if the star is above the horizon; it is negative if the star is below the horizon. Altitude combined with azimuth can specify the position of any object in the sky. Find the altitudes and azimuths of some reference points on the celestial sphere and complete the following table (Table A.1). If a blank space cannot have any value for the entry, indicate this by putting an × in the appropriate blank. The Celestial Globe In this part of the activity, you will work with a celestial globe, which is simply a clear sphere made of plastic on which bright stars are painted. The stars are arranged in such a way that if you are located at the center of the globe, you would see the same arrangement as you would see in the real sky. The fact that all of CHAPTER A. IN-CLASS ACTIVITIES 5 Zenith Vertical Circle ★ Altitude N W E H S Azimuth Nadir Figure A.3: Azimuth and altitude. Table A.1: Azimuth and azimuth of celestial reference points and circles. Point or Circle Azimuth Altitude North point 0◦ 0◦ 90◦ 0◦ 0◦ to 360◦ 0◦ × −90◦ 315◦ 0◦ South point West point Celestial meridian Horizon Zenith Southeast point 6 CHAPTER A. IN-CLASS ACTIVITIES the stars are painted on the globe’s surface should not be interpreted to mean that they are all at the same distance from the Earth because they are not. The celestial globe only represents the directions of the stars with respect to the observer at the center. The celestial globe should be rotated in the clockwise direction as seen from above the north pole. The Earth’s is actually rotating in the counterclockwise direction by 15◦ every hour. But with respect to the observer standing on the surface of the Earth, the celestial sphere appears to rotate in the opposite direction. With the aid of the celestial globe, the stars can be made to move just as they do when observed from the Earth. ① Orient the celestial globe so that its north pole is at an angle of about 37.1◦ (which is the latitude of Radford) above the north point on the horizon. The horizon is represented by the horizontal metal ring in the frame that supports the celestial globe. ② Your instructor will specify the orientation of the globe by giving you an hour angle. These angles are marked just above the celestial equator at the crossing of each meridian. Rotate the globe until this hour angle lies under the vertical metal ring that supports the globe. This vertical ring represents the local celestial meridian. If you are uncertain about the proper orientation of the globe or its use, consult with your instructor. ③ Record in Table A.2 the azimuth and altitude of the stars listed there. Be sure that the celestial globe is properly oriented and that it is not disturbed during the measurement. Table A.2: Azimuth and altitude of bright stars on the celestial globe. Star Name Azimuth Altitude Vega Fomalhaut Sirius Arcturus Capella Antares Canopus The Equatorial System Before we learn about the equatorial system of coordinates, we need to define a few more reference points and circles in the sky. You are undoubtedly aware of the rising and setting of the stars. However, you may not be aware that the stars appear to be rotating about a fixed point in the sky directly above the north point on the horizon. This fixed point is called the north celestial pole (NCP). The north celestial pole is in the direction of the Earth’s rotational axis, and it is the point on the celestial sphere directly above the Earth’s geographic north pole. The apparent motion of stars around the north celestial pole is due to the rotation of the Earth. There is a bright star called Polaris approximately at the location of the north celestial pole. The corresponding point in the the sky south of the Earth’s equator is the south celestial pole (SCP). CHAPTER A. IN-CLASS ACTIVITIES 7 The only difference is that the stars appear to rotate counterclockwise about the north celestial pole but clockwise about the south celestial pole. The altitude of the north celestial pole is equal to the latitude of the observer’s location. For example, the north celestial pole is located at 37.1◦ altitude (and obviously 0◦ azimuth) in Radford. Zenith Celestial Equator NCP W S 37.1º N Observer Horizon E SCP Nadir Figure A.4: Celestial poles and equator. The circle on the celestial sphere which is 90◦ from both the NCP and the SCP is the celestial equator. The celestial equator is the imaginary circle around the sky directly above the Earth’s equator. Figure A.4 illustrates the relationship of the NCP, SCP and celestial equator to the alt-azimuth system discussed earlier. In order to set up a system of coordinates on the celestial sphere, it is necessary to specify both a reference point and a reference circle. In the alt-azimuth system, the north point and the horizon were chosen. For the equatorial system, the celestial equator serves as the reference circle. The reference point is set on the vernal equinox, which is the point on the celestial sphere where the Sun crosses the celestial equator moving northward. The apparent path of the Sun around the sky is called the ecliptic. The circles on the celestial sphere which pass through both celestial poles and cross the celestial equator at right angles are called hours circles (see Fig. A.5). The hour circles which passes through the vernal equinox is labeled 0h . Every successive 15◦ interval measured along the celestial equator constitutes 1h . The right ascension (RA) of a star is the angular distance measured in hours, minutes, and seconds from the hour circle of the vernal equinox (0h ) eastward along the celestial equator to the the point of intersection of the star’s hour circle with the equator. The star’s declination (Dec.) is the angle measured along its hour circle from the celestial equator. The declination is positive for an object north of the celestial equator and negative for an object south of the equator. The declination is 0◦ everywhere on the celestial circle. The main advantage of the equatorial system is that it is independent of the observer’s location because it does not depend on the locally defined horizon. The equatorial coordinates are fixed on the celestial sphere and move with stars. If one expresses the position of a star in the sky in terms of RA and Dec., another observer anywhere else on the Earth, is able to locate the star. ① Assume that the vernal equinox is on the local celestial meridian. Determine the right ascension and declination of points listed in the following table (Table A.3). If an entry cannot have any value, put an × in the appropriate blank. The celestial globe might be helpful to finds the coordinates. 8 CHAPTER A. IN-CLASS ACTIVITIES Vernal Equinox SCP NCP 0h 1h 2h Hour Circles Celestial Equator Figure A.5: Hour circles. NCP Vernal Equinox Star's Hour Circles RA ★ Dec. SCP Celestial Equator Figure A.6: Right ascension and declination. CHAPTER A. IN-CLASS ACTIVITIES Point Zenith 9 Table A.3: RA and Dec. of points on the celestial Sphere. RA Dec. h 0 +37◦ NCP North point East point South point West point SCP Nadir ② Using a celestial globe, determine the RA and Dec. of the stars listed in Table A.4. The RA scale is marked along the celestial equator on the globe, and the Dec. scale is indicated beside the declination circles. Table A.4: RA and Dec. of bright stars on the celestial globe. Star Name RA Dec. Vega Fomalhaut Sirius Arcturus Capella Antares Canopus V. Questions 1. Would you say that a star’s azimuth and altitude remain fixed throughout the course of an evening? Explain. 10 CHAPTER A. IN-CLASS ACTIVITIES 2. Would an observer at a different location observe the same azimuth and altitude for a particular star if he were observing at the same time as you? Explain. 3. Is there a point on the celestial sphere at which an object’s azimuth and altitude would not change in the course of an evening? If so, describe this point. 4. Can you think of a possible shortcoming in using the alt-azimuth system of coordinates if you were interested in communicating information regarding the position of a comet to an observe located in a different part of the world? CHAPTER A. IN-CLASS ACTIVITIES 11 Name: A.2 I. Section: Date: Angular Resolution: Seeing Details with the Eye Introduction We can see through a telescope that the surface of the Moon is covered with numerous impact craters of various sizes. Some craters are hundreds of kilometers across; some are less than one millimeter. But, what is the diameter of the smallest crater that you can seen on the Moon with your naked eyes? In this activity you are going to determine the smallest separation that your eyes can see at a given distance. II. Reference • The Cosmic Perspecive, Chapter 7, p. 174, 180 - 181 III. Materials Used • fantailed chart • meter stick • blank sheet IV. Activities One measure of the performance of a telescope is its angular resolution. Angular resolution refers to the ability of a telescope to distinguish between two objects lying close together in the sky. The finer the resolution, the better we can tell the objects apart. 1. Tape the “fantailed” chart (Fig. A.8) to a wall in a well-lit classroom. 2. Stand 10 m from the chart. 3. Your partner will hold a sheet of paper over the chart, hiding all but the bottom tip. Tell your partner to move the paper very slowly up the chart, keeping the paper horizontal. When you start to see the chart lines clearly separated from each other just below the paper, tell your partner to hold the paper in place. 4. Your partner will read the line spacing printed on the chart nearest to the top of the paper. Table A.5: The distance-to-size ratio for your eye. distance line spacing distance-to(m) value (mm) size ratio 10 15 5. Repeat the measurement at 15 m. 12 CHAPTER A. IN-CLASS ACTIVITIES Suppose when your classmate stood 10 m (= 10,000 mm) from the chart, she was just able to distinguish the separation of the lines spaced 4.5 mm apart. The distance-to-size ratio for her eyes is 10,000 mm (the distance to the chart) divided by 4.5 mm (the line spacing): 10, 000 mm 2, 200 = . 4.5 mm 1 (A.1) This ratio can be written as 2,200/1, the distance-to-size ratio for her eyes. This ratio is read as “2,200 to 1” and can also be written as 2,200:1. The larger the distance-to-size ratio, the more detail your eyes can see. 5. Calculate the distance-to-size ratio for your eyes. 6. Repeat the measurement of the distance-to-size ratio for 15 m from the chart. How do the two ratios compare? 7. Find the average of two measurements for your distance-to-size ratio. You will be using this average value for the problems in the Questions section later. The distance-to-size ratio for your eyes determines how much detail you can see. Using the triangle method, you can estimate the “sharpness” (ability to see detail) of your eyesight. In Fig. A.7, O is the position of your eyes; A and B are two side-by-side lights. The distance of the observer from the lights is OA (or OB); the distance (i.e., size) between the lights is AB. In the previous example, your classmate had the distance-to-size ratio of 2,200/1. This ratio means that if she were closer than 2,200 m away from two lights separated by 1 m, she would see two separate lights. If she were farther away than 2,200 m, she would not be able to distinguish the two lights; she would see only one light. V. Questions 1. What is the farthest distance you could be from two lights, separated by 1.0 cm, and still see them as two lights? 2. What is the farthest distance you could be from two lights, separated by 30 m, and still see them as two lights? CHAPTER A. IN-CLASS ACTIVITIES 13 ✩ Light A O Eye ✩ Light B Figure A.7: Sharpness of your eyesight. 3. Will you be able to distinguish two lights separated by 50 cm if you were standing 500 m from them? Show your work. 4. An automobile has headlights placed 1.2 m apart. If the car were driving toward you at night, how close to you would it have to be for your to tell it was a car and not a motorcycle? 5. The Moon is about 384,000 km from the Earth. What is the diameter of the smallest crater that you could see on the lunar surface? 14 CHAPTER A. IN-CLASS ACTIVITIES 6.0 mm 5.5 mm 5.0 mm 4.5 mm 4.0 mm 3.5 mm 3.0 mm 2.5 mm 2.0 mm 1.5 mm 1.0 mm 0.5 mm Figure A.8: The fantailed chart for measuring the distance-to-size ratio. CHAPTER A. IN-CLASS ACTIVITIES 15 Name: A.3 I. Section: Date: Estimating the Diameter of the Sun Introduction Take notice of the round spots of light on the shady ground beneath trees. These are sunballs—images of the Sun. They are cast by openings between leaves in the trees. The diameter of a sunball depends on its distance between the small opening and the screen. Large sunballs, several centimeters in diameter or so, are cast by openings that are relatively high above the ground, while small ones are produced by those closer to the ground. From geometry, the ratio of the diameter of the sunball to its distance from the pinhole is the same as the ratio of the Sun’s diameter to its distance from the pinhole. Sunball Pinhole D Sun L Ground d l Figure A.9: A sunball created by a pinhole. In this lab you will use a mirror, instead of a pinhole, to cast a bright image of the Sun on a wall as shown in Fig. A.10. Wall d Sunball l D Sun Mirror L Figure A.10: A sunball created by a mirror. From the known distance between the Sun and Earth, careful measurement of the distance-to-size ratio tells us the diameter of the Sun. 16 CHAPTER A. IN-CLASS ACTIVITIES II. Reference • 21st Century Astronomy, Chapter 13 III. Materials Used • small, flat mirror • large piece of paper • marker • ruler • masking tape • tape measure IV. • sunny day Safety and Disposal Do not directly stare at the Sun or at the image in the mirror. V. Activities ① Take the mirror outside. Stand so you are facing, and at least 15 m away from, the shaded wall of a building. The Sun must also be visible either in front of you or to your side. ② Position the mirror so it reflects an image of the Sun on the wall you are facing. ③ Tape a large piece of paper at the position where the Sun’s image is formed on the wall. ④ Hold the image steady so that the image is at the center of the paper. Your partner will use the marker to trace the outline of the reflected image of the Sun on the paper. ⑤ Measure the distance between the mirror and the Sun’s image in centimeters using the tape measure. Table A.6: Measuring the distance-to-size ratio for the Sun. distance to diameter of the wall the Sun’s (cm) image (cm) ⑥ Measure the diameter of the outline in centimeters using the ruler. VI. Questions 1. Calculate the number of solar image diameters that, if placed “end-to-end,” would fill the distance between the mirror and the wall. CHAPTER A. IN-CLASS ACTIVITIES 17 2. The ratio of the distance (l) between the mirror and the wall to the diameter (d) of the solar image is equal to the ratio of the distance (L) between the Sun and Earth to the solar diameter (D). l L = . d D How many solar diameters is the Sun from the Earth? 3. Given that the Sun is 150,000,000 km from the Earth, calculate the diameter of the Sun. (A.2) 18 CHAPTER A. IN-CLASS ACTIVITIES Chapter B Laboratory Experiments 19 20 CHAPTER B. LABORATORY EXPERIMENTS CHAPTER B. LABORATORY EXPERIMENTS Name: B.1 I. 21 Section: Date: Optics and Spectroscopy Introduction Until the introduction of the telescope to astronomy, all observations had been done with naked eye observations. This limited the resolution and magnification with which we could resolve details on objects even as near as the Moon. In addition, the number and type of objects which could be observed was also limited due to the amount of light the human eye can detect. Those objects with an apparent magnitude of 6 or greater could not be seen. Galileo was the first person to construct a telescope and use it for astronomical purposes and he immediately made many important discoveries. Probably the most famous of these early observations was his discovery of four moons of Jupiter, now known as the Galilean moons. Galileo observed Io, Europa, Callisto, and Ganymede and noticed that they orbited Jupiter, not the Earth. This was one of the final straws in the geocentric theory of the solar system. Today even with the ability to look at almost any wavelength in the spectrum of light, optical telescopes (those which look at the visible portion of the spectrum) are still one of the most fundamental and useful tools for the professional astronomer and the only reasonably affordable tool for amateurs. Light comes in a wide variety of frequencies (or equivalently wavelengths) from x-rays to radio waves. The visible spectrum is but a small portion of the total information available to astronomers. However one can still gain a great deal of information by breaking a beam of light into its component pieces by frequency (or wavelength). You have probably seen this process using a prism which takes white light from the Sun or a light bulb and spreads it out into a range of colors from red to violet. Astronomers use the brightness at each of these wavelengths to determine a great deal about the object they are observing. One of the most important pieces of information they can obtain by looking at the spectrum is the composition of the object. This process is known as spectroscopy. In this lab today you will learn some of the basic optical rules for constructing telescopes and how astronomers use spectroscopy to determine the composition of the object they are observing. II. Reference • 21st Century Astronomy, Chapter 4, p. 103 –113 III. Materials Used • light box • concave lens • 200 W bulb • 3 x 5 index card • mirror • protractor • diffraction grating goggle • spectral tubes • convex lens • spectral tube power supply IV. Safety and Disposal Do not look directly at the Sun or any other bright light source. 22 CHAPTER B. LABORATORY EXPERIMENTS V. Experiments Optical telescopes Optical telescopes come in two varieties, either reflecting or refracting. Reflecting telescopes use a mirror to focus the incoming light from the sky to an eyepiece or camera for observation. They are the most commonly used type of telescope today as they are easier to construct for large or very large telescopes and are relatively cheaper than producing a refracting telescope of the same size. A refracting telescope uses lenses to focus the incoming light to the eyepiece or camera. While refractors have their advantages, making very accurate and non-distorting lenses of even moderate size is a fairly expensive undertaking. With a mirror you have only one surface to make precisely whereas with a lens you must insure that both surfaces of the lens is precise and that the lens is clear and uniform throughout the body of the lens. Today you will investigate the basic principles behind the assembly of a reflecting telescope including determining how light reflects from the surface of the mirror and what happens to the orientation of an object seen in a mirror and how that changes with the number of reflections. You will also determine what happens to the orientation of an image as seen through various types of lenses. ① Obtain a light box, 200 W bulb and a flat mirror. ② Place one of the black sheets with slits over the appropriate window on the side of the box. Insure that the slit is narrow for greater ease of measurement. ③ In the area below, place the mirror vertically along the indicated line. ④ Using the light box, direct a beam of light so that it strikes the mirror at an angle at the intersection of the plane of the mirror and the dotted perpendicular line. Carefully sketch the direction of the incoming and the reflected beam of light and label each respectively. You may find it easiest to use the center of the beam of light to sketch the beams. Mirror Figure B.1: Reflection of a beam of light by a mirror. ⑤ Using a protractor, carefully measure the angle of the light beam from the perpendicular line, commonly referred to as the normal, for both the incoming and reflected beams and record these angles in Table B.1 below. ⑥ Repeat the previous two steps after moving the light box so that the incoming beam approaches the mirror at a different angle and again record the measurements in Table B.1 below. CHAPTER B. LABORATORY EXPERIMENTS 23 Table B.1: Angles of incidence and angles of reflection. Trial Incoming Reflected Angle (◦ ) Angle (◦ ) Trial # 1 Trial # 2 ⑦ From your data, what can you infer about the relationship between the incoming angle and the reflected angle of the beam of light? ⑧ Now place the mirror in the space below on the upper horizontal line with the reflecting surface facing you. Looking solely in the mirror, attempt to write your name on the line below the mirror. Mirror ⑨ Placing the mirror below in the same orientation as before, draw 4 arrows (one each pointing up, down, left, and right) as seen in the mirror. Compare these to the directions as shown on the piece of paper. Mirror ⑩ Using the information from above, what can you say about the orientation of direction as seen with the naked eye as that compared to the orientation as seen from a single reflection from a mirror. What do you think would happen if you had 2 reflections? Three? 24 CHAPTER B. LABORATORY EXPERIMENTS Lenses ① Obtain a 3 × 5 index card, a convex lens, and a concave lens. On the card draw a large arrow. ② Have your partner hold the arrow vertically while you hold the convex lens in the line of sight between your eye and the arrow. Move the lens back and forth until the arrow is focused. What is it’s orientation? ③ Have your partner rotate the arrow to point horizontally and again observe the orientation of the arrow through the convex lens. What is the orientation of the arrow now? ④ Repeat the above two steps for the concave lens noting the orientation of the arrow in both positions ⑤ Using the information from above, summarize what the concave and convex lenses do to the images (orientation and size). Spectral lines Spectroscopy is one of the most important tools astronomers have in the study of the heavens. By understanding the spectrum taken from an object, astronomers can understand that object’s composition, rotation, and temperature. Spectral lines appear primarily due to transitions of electrons between orbitals in atoms. The differences in energy between the energy levels of the electron cause the appearance of lines at different wavelengths (or energies). In this portion of the lab you will observe a number of known spectra and then use those spectra to identify an unknown spectrum. ① Obtain a diffraction grating for each group member. Observe the five different known spectra. Sketch those spectra in the boxes in Fig. B.2. Be sure to label the colors of each line. ② Have your instructor insert the unknown gas into the transformer and observe it with your diffraction grating. Sketch the unknown spectrum in the box in Fig. B.3, again labeling each line’s color. ③ Compare your unknown spectrum with the known spectra and identify the composition of the unknown. CHAPTER B. LABORATORY EXPERIMENTS 25 Element: Violet Blue Green Yellow Orange Red 400 nm 450 nm 500 nm 550 nm 600 nm 650 nm Element: Violet Blue Green Yellow Orange Red 400 nm 450 nm 500 nm 550 nm 600 nm 650 nm Element: Violet Blue Green Yellow Orange Red 400 nm 450 nm 500 nm 550 nm 600 nm 650 nm Element: Violet Blue Green Yellow Orange Red 400 nm 450 nm 500 nm 550 nm 600 nm 650 nm Element: Violet Blue Green Yellow Orange Red 400 nm 450 nm 500 nm 550 nm 600 nm 650 nm Figure B.2: Spectra of known elements. 26 CHAPTER B. LABORATORY EXPERIMENTS Element: Violet Blue Green Yellow Orange Red 400 nm 450 nm 500 nm 550 nm 600 nm 650 nm Figure B.3: Unknown spectrum. VI. Questions 1. Explain briefly how an astronomer can determine if the object being observed is moving along the line of sight by simply looking at the spectrum from the source. 2. A common type of telescope is known as a Cassegrain telescope. This is a reflecting telescope and consists of a primary mirror which collects the incoming light from the object and bounces it to a secondary mirror which then reflects the light through a simple eyepiece consisting of a single convex lens. While looking at an object through this telescope, how would the image seen through the eyepiece compare with that seen by the naked eye? VII. Credit To obtain credit for this lab, you need to include your sketches using the mirrors, your conclusions about how lenses affect the orientation of objects and your sketches of the known and unknown spectra, the identification of your unknown, and the answers to the above questions. CHAPTER B. LABORATORY EXPERIMENTS 27 Name: B.2 I. Section: Date: Magnets: Magnetic Force and Magnetic Field Introduction People have known about magnets and their properties for a long time. Magnets can attract each other, but they can also repel each other. The ancient Chinese used magnets as navigation tools. Today magnets of many different sizes are widely used. For example, a magnet can hold a memo on a refrigerator. Also, a small magnet inside a computer hard disk is used to record vital information, such as your term paper. In this lab we will study properties of magnets. II. Reference • Astronomy Today, Chapter 7, pp. 157 – 162. III. Materials Used • bar magnet • round magnets • magnetic compass • paper clips IV. • glass plate • saran wrap • iron filings Safety and Disposal Do not directly touch iron filings with a magnet. V. Experiments What Kinds of Material Are Attracted to Magnets? Some materials are attracted to a magnet, but some aren’t. In this part of the lab, you are going to test ten different materials in the classroom to determine whether they are attracted to a magnet or not. You need to test at least three different types of metals, because not all metals are attracted to magnets. Magnetic Force Through Materials ① Place a paper clip on a sheet of paper. Hold a magnet beneath the sheet and move the magnet around? What happens to the clip on top? 28 CHAPTER B. LABORATORY EXPERIMENTS Table B.2: Which materials are attracted to a magnet? material attracted? material attracted? (Y/N) (Y/N) penny eraser Table B.3: A magnet can exert a force through materials. material attracted? (Y/N) glass plate cloth Saranwrap CHAPTER B. LABORATORY EXPERIMENTS 29 ② Try with another material, such as aluminum foil, a glass plate, a piece of cloth, a piece of Saranwrap, etc., and observe whether the the clip and magnet are still attracted to each other. Magnetic Compass A magnetic compass is just a small magnet suspended on a fluid for freedom of rotation. The north pole of the compass is attracted to the south pole of a nearby magnet, which could be the Earth. Many celestial objects, such as the Earth and the Sun, behave like magnets. ① Place a magnetic compass on a table. It should point toward the magnetic south pole of the Earth which is located near the geographic north pole of the Earth. ② Bring a magnet close to the compass and move it around. Describe what happens to the direction the compass points. The south pole of the magnet will attract the north pole of the compass. ③ Flip the magnet and record what happens to the compass. Magnetic Field Around a magnet there exists a region of magnetic influence called the magnetic field. We can tell there is a magnetic field because magnets can exert forces over a distance. We can see the pattern of the magnetic field by sprinkling iron filings on a sheet of paper placed above a magnet. ① Place a sheet of white paper on a magnet. Place notebooks or something beneath to support the edges of the paper so that it stays flat. ② Sprinkle iron filings on the paper. The filings will line up in the direction of the magnetic field and form a geometric pattern. Sketch the pattern. ③ Repeat the experiment with the same magnet but now on its side or with another magnet of different shape. Sketch the magnetic field. Mapping a Magnetic Field Around a Bar Magnet We will use a compass to investigate the magnetic field of a bar magnet. The direction of the magnetic field at any point is the direction in which the north pole of a compass needle points when placed at that location. A line whose tangent is in the direction of the field at every point is called a magnetic field line. The relative spacing of lines indicates the relative intensity of the field. The closer the field lines, the stronger the field. ① Bring one end of a bar magnet near the north end of the compass. Note the direction of the needle. Is it deflected toward or away from the magnet? Turn the magnet around. In which direction is the 30 CHAPTER B. LABORATORY EXPERIMENTS Figure B.4: Magnetic field around a magnet. Figure B.5: Magnetic field around a magnet. CHAPTER B. LABORATORY EXPERIMENTS 31 deflection now? Since like poles repel and unlike poles attract, you should now be able to tell which end of your bar magnet is north and which is south. ② Place a bar magnet in the center of the sheet with its north-south axis aligned with the Earth’s magnetic field. Better results are obtained if the south pole of the bar magnet points north. N Compass S W E N S Figure B.6: Mapping magnetic field around a bar magnet. ③ Now determine the field lines using the compass. Mark a dot near the south pole of the magnet. Place the back of the compass on this dot in such a way that the south pole of the needle points toward the dot. The north pole of the needle then gives the next point on the field line. Mark this with a dot and then continue by placing the south pole at the second dot. ④ Join the dots by a smooth curve. Trace out in this fashion several complete field lines. Put one or more arrow on a line to indicate the direction of the field. VI. Questions 1. Can you separate the north and south poles of a magnet? 32 CHAPTER B. LABORATORY EXPERIMENTS 2. In your field map for the bar magnet, where is the field the strongest? The weakest? 3. Where do field lines start and end? VII. Credit To receive credit on this lab, you must turn in all of your observations from the experiment in Tables B.2, B.3 as well as two sketches of magnetic fields and the map of magnetic field around the bar magnet. Please discuss possible sources of error in the experiment. Finally, you need to also include answers to the above questions. CHAPTER B. LABORATORY EXPERIMENTS Name: B.3 I. 33 Section: Date: Brightness and Distance Introduction Previously (in Astronomy 111) you used triangulation to determine distances to planets and stars. This method is effective only for relatively close (< 1, 000 light years) objects. For much farther objects, their parallaxes become so small that we can no longer determine their distances very accurately. The second method for estimating astronomical distances uses the easily observed fact that the farther away a light source is, the dimmer it appears. If you know how bright an object would appear at a certain distances from you, and you can measure how bright it does appear, you can determine its distance from you. In this lab your are going to learn how this principle works quantitatively. II. Reference • 21st Century Astronomy, Chapter 4, p. 121-2, Chapter 12, p. 308 III. Materials Used • 200-W clear bulb • 2 pieces of 20 × 25 cm cardboard • meter stick • scissors • grid paper (or coarse graph paper) • cutter knife • black mask with a square whole • masking tape IV. Safety and Disposal Do not touch the bulb. It gets very hot! V. Experiments Brightness vs. distance In this experiment you are going to determine the quantitative relationship between the brightness and distance using a light bulb. 1. Cut a 5-cm diameter hole from the center of a piece of cardboard. Carefully cut out the small white square on the black mask. Tape this sheet onto the piece of cardboard so that the square is over the hole. 2. Tape the grid sheet to the other piece of cardboard. 3. Turn on the 200-W bulb and turn off the room lights. Hold the single square opening at a distance of 10 cm from the bulb. Make sure this piece of cardboard is perpendicular to the bulb’s filament. 4. Now place the grid sheet against the square opening. Line up a square on the sheet with the square opening. 34 CHAPTER B. LABORATORY EXPERIMENTS One square hole (remains at 10 cm) 10 cm Light from end of filament Bulb Mask Grid Sheet Distance from Bulb Figure B.7: Measuring the brightness of a bulb at various distances. 5. The light coming through the square opening is now illuminating one square on the grid sheet. Record a number “1” for the distance of 10 cm in Table B.4. Table B.4: Measuring the number of illuminated squares at various distances. distance from number of fraction of light bulb (cm) illuminated on each square squares 10 20 30 40 6. While your partner holds the square at a distance of 10 cm from the bulb, move the grid sheet to a distance of 20 cm from the bulb. Keep the cardboard with the square hole and the cardboard with the grid parallel to each other. Be sure the end of the filament is pointed at the opening. 7. Count the number of squares on the grid illuminated by the light passing through the square opening. Record this number in Table B.4. 8. Repeat Steps 6 and 7 for distances 30 cm and 40 cm from the bulb, and record the number in the table. 9. For each distance, calculate the fraction of light passing through the square opening that falls on one of the illuminated squares. Record the fractions in Table B.4. 10. Using the results from the last part, complete Table B.5 to a distance of 100 cm. CHAPTER B. LABORATORY EXPERIMENTS 35 Table B.5: Fraction of light reaching one square on the grid sheet at various distances. distance (cm) 10 20 30 40 50 60 70 80 90 100 fraction of light on one square Brightness vs. number of bulbs Now we want to determine the number of bulbs at different distances that would produce the same brightness as one bulb at 10 cm. Refer to Table B.5 to answer the following questions. 1. How many identical bulbs would have to be placed at the position of the original bulb for a square on the grid sheet at a distance of 20 cm to be as bright as it was at 10 cm? 2. How many identical bulbs would have to be placed at the position of the original bulb for a square on the grid sheet at a distance of 50 cm to be as bright as it was at 10 cm? 3. How many identical bulbs would have to be placed at the position of the original bulb for a square on the grid sheet at 9 times the original distance to be as bright as it was 10 cm? 4. Using the results from the preceding discussion, complete Table B.6 to a distance of 100 cm. This table is similar to Table B.5 except that it show the number of identical light bulbs at various distances that would produce a brightness equal to that of one bulb at 10 cm. Table B.6: Number of bulbs producing the same brightness as one bulb at 10 cm. distance (cm) 10 20 30 40 50 60 70 80 90 number of bulbs 100 Varying both distance and number of bulbs Now we are going to change the distance between the bulbs and the grid sheet and the number of bulbs at the same time. Use Table B.6 to answer the following questions. Assume that all the bulbs are identical. 1. How many bulbs at 30 cm will produce the same brightness as 1 bulb at 10 cm? 36 CHAPTER B. LABORATORY EXPERIMENTS 2. How many bulbs are needed to produce the same brightness as one bulb when they are at 5 times the original distance of the one bulb? 3. How many bulbs will produce the same brightness at 10 times the original distance for one bulb? 4. How many bulbs would you have to place at a distance of 100 m from you to produce the same brightness as one bulb at a distance of 25 cm? Show your work. 5. How many bulbs would you have to place at 1 km to produce the same brightness as one bulb at 50 cm? Show your work. VI. Questions 1. Mars is 1.5 times farther from the Sun than the Earth. How would the brightness of the Sun at Mars compare to its brightness as seen from the Earth? 2. Neptune is 30 times farther from the Sun than the Earth. How would the brightness of the Sun at Neptune compare to its brightness as seen from the Earth? 3. Mercury is 4/10 as far from the Sun as the Earth. How would the brightness of the Sun at Mercury compare to its brightness as seen from the Earth? 4. If the Sun were to becomes 100 times more luminous than it is, how far would we have to go away from the Sun so that it would appear as bright as it normally does? VII. Credit To receive credit on this lab, you must turn in all of your data from the experiment in Tables B.4, B.5, and B.6, and answers to the questions within the experiments. Finally, you need to also include answers to the questions at the end of the lab. Cut out this small square carefully. CHAPTER B. LABORATORY EXPERIMENTS 39 40 CHAPTER B. LABORATORY EXPERIMENTS CHAPTER B. LABORATORY EXPERIMENTS Name: B.4 I. 41 Section: Date: How Many 200W Light Bulbs Does It Take to Equal the Sun? Introduction In this lab you will construct a simple photometer. A photometer is a device that measures the brightness of light. As an observer moves away from a source of light, the brightness of the light source appears to decrease. You will use the information you discover on how the brightness decreases to estimate the number of 200-W light bulbs it would take to have the same brightness as the Sun. II. Reference • 21st Century Astronomy, Chapter 13 III. Materials Used • 1 paraffin block, 6 cm × 12 cm • one unfrosted 200-W light bulb • 1 piece of aluminum foil, 6 cm × 12 cm • meter stick • two rubber bands • nail or scissors • one unfrosted 100-W light bulb • extension cord IV. Safety and Disposal Do not touch the bulbs while or shortly after they are on as they will be very hot. V. Experiments Construct and test a photometer ① Take your piece of paraffin. You will actually want two 6 cm × 6 cm pieces. Use a nail or tip of a pair of scissors to to scratch a mark into the paraffin, dividing it into two equal-sized pieces. Align the paraffin on the edge of the desktop so that the scratch is along the edge. Pull down on the overhanging piece to break the paraffin evenly into two pieces. Do not strike the paraffin as it will break unevenly. ② Fold the piece of aluminum foil in half so that the shiny sides face outwards. Place the foil between the two blocks or paraffin and use rubber bands to hold it all together. This is your photometer. ③ Darken the room as much as possible and place the 200-W light bulb 1 meter from your photometer as in Figure B.8 below. By looking at the side (as shown in the figure) you can compare the difference between the side with the light bulb and the side without. Compare the brightnesses of the two sides. 42 CHAPTER B. LABORATORY EXPERIMENTS 200-W light bulb Photometer Figure B.8: Photometer and light bulb arrangement. ④ Place the 100-W light bulb at a distance of 0.5 meters from your photometer. Place the 200-W light bulb on the other side of the photometer also at a distance of 0.5 meters. Again, observe from the side and compare the brightness on each side of the photometer with each other. ⑤ How far away do you think you’ll need to move the 200-W bulb to create the same brightness as the 100W bulb (leaving the 100-W bulb at 0.5 meters)? ⑥ Leaving the 100-W bulb at 0.5 meters, move the 200W bulb until the photometer shows equal brightnesses on both sides. To what distance did you have to move the 200-W bulb? ⑦ Now imagine that the 100-W bulb was only 0.25 meters (25 cm) from the photometer. Where would the 200-W bulb have to be placed to have equal brightness? Is there a relationship between these distances? If so, what is the relationship? CHAPTER B. LABORATORY EXPERIMENTS 43 Measuring the Sun’s luminosity The luminosity is a measure of the brightness of an object measured in terms of the total power it puts out. The intensity of the light (the brightness) decreases with distance as you saw earlier, even though the total power of the light bulb was not changing. You will use this fact and the relationship of the luminosity to the brightness that you found earlier to measure the luminosity of the Sun. ① On a bright, sunny day, take your photometer and 200-W bulb outside along with an extension cord and a meter stick. ② Hold the photometer between the Sun and the bulb. Hold the bulb so that its filament is parallel to the plane of the photometer. Observe the photometer as before. You will probably note a color difference between the two sides. Describe that below. This will make it more difficult to compare brightnesses so observe very carefully. ③ One partner hold the photometer and move it so that the brightness on both sides is identical. Measure the distance from the 200-W bulb to the front of the photometer. Repeat this 3 more times, making sure that each member observes at least once and complete Table B.7 below. Trial # 1 Distance (cm) 2 3 4 Average Table B.7: Photometer Data Table ④ The Sun is approximately 1.5 × 108 km from the Earth. How many centimeters is that? ⑤ How many times bigger is this distance than the distance from the photometer to the 200-W bulb? 44 CHAPTER B. LABORATORY EXPERIMENTS ⑥ Using the relationship between distance and luminosity you found earlier, how much brighter is the Sun than the 200-W bulb? ⑦ What is the total luminosity of the Sun? In other words, how many 1-W bulbs does it take to equal the Sun’s luminosity? VI. Questions 1. If you had a 100-W light bulb located at a distance of 1 meter from your photometer, where would you have to place a 300-W light bulb to see the same brightness? 2. Mars is about 1.5 times further from the Sun than Earth is. If you repeated this experiment on Mars, how far away would you need to hold the photometer from a 200-W bulb to obtain the same brightness as that from the Sun? CHAPTER B. LABORATORY EXPERIMENTS VII. 45 Credit To receive credit for this lab, you need to turn in all of your calculations and data in addition to the answers to the above questions. 46 CHAPTER B. LABORATORY EXPERIMENTS Chapter C Computer Laboratories (CLEA) 47 48 CHAPTER C. COMPUTER LABORATORIES (CLEA) CHAPTER C. COMPUTER LABORATORIES (CLEA) Name: C.1 I. 49 Section: Date: The Classification of Stellar Spectra Introduction Patterns of spectral lines have been used to catalog stars for over a century. The Harvard classification scheme, known as the Henry Draper Catalog, uses seven major spectral classes, O, B, A, F, G, K, and M, which ranks stars by temperture from hotter to colder respectively. These major classes are subdivided further into tenths (from 0-9). For example, the Sun is a star of type G2. As with the magnitude scale, a smaller number actually indicates a hotter object. This means for example that a B0 star is the hottest B-type star, while a B9 is the coolest. The current system is a refinement of the Harvard system, known as the MK system. This system adds a further refinement, a luminosity class, which is represented by a Roman numeral to the end of the spectral type. This refinement arised because astronomers learned that stars with the same temperature could have vastly different sizes. The luminosity classes are: I III V supergiant giant star main sequence The spectral type of a star is an important piece of information, so much so that it is the very first thing an astronomer will find out upon beginning to observe a star. If the star’s spectral type is not already known, the classification will have to be measured. In this lab, we will do this by simulating the process of taking spectra from various stars and matching them to a catalog of well-studied spectra. The classification of stars allows astronomers to learn a great deal about the star. In addition to its temperature, the star’s luminosity, color, distance, and mass can be determined, along with information about the star’s evolutionary history. This lab will consist of two sections. In the first section, you will learn to classify spectra by taking spectra from a set of stars and comparing the observed spectra to a catalog of well-known spectra of classified stars. In the second portion of the lab, you will take spectra for two unclassified stars and use your information to calculate the distance to each star. II. Reference • CLEA Stellar Spectra Lab, http://www.gettysburg.edu/ academics/physics/clea/CLEAhome.html • The Cosmic Perspetive, Chapter 16, p. 526 – 529 III. Materials Used • CLEA Stellar Spectra program IV. • calculator Observations The observations you will be doing are simulated observations of stars using the CLEA program. You will do the following things in this observation: 50 CHAPTER C. COMPUTER LABORATORIES (CLEA) • take the spectra of 25 stars and classify them using a catalog • take the sepctra of 2 unknown stars, classify them and using that information determine the distance to both stars Observation 1. Start the Spectra Classification lab by double-clicking on the Clea spe icon. 2. Log in to the program by entering your name into the appropriate place after selecting Log In from the File menu. 3. Select Classify Spectra from the File menu. 4. To display the spectra of a practice unknown star, select File in the the new window. Choose Unknown → Program List → HD 124320. Click OK to display the spectrum of this star. 5. The spectrum will appear in the window. Note that the spectrum is shown as taken by a digital spectrometer. The highest points in the curve are called the continuum and are the overall light coming from the surface of the star. The dips are absorption lines produced by cooler atoms or molecules above the surface of the star. The strength of the absorption can be seen by the depth and the width of the line. You can measure the wavelength and intensity of the light at any point in the spectrum by pointing the cursor at it and clicking the left mouse button. In this lab, wavelengths are ˙ which is equivalent to 10−10 m. measured in Angstroms (A) 6. Choose any point on the continuum of HD 124320 and record its wavelength and intensity below. Do the same for the deepest portion of the deepest absorption line and record that information. continuum wavelength intensity absorption line wavelength intensity 7. Now you want to find the spectral type of HD 124320 by comparing its spectrum to that of known stars. To do so, use the comparison star atlas by selecting File → Atlas of Standard Spectra. Choose the Main Sequence option and then click Ok to load the atlas. 8. The 13 spectra in the atlas will appear in a separate window, but only 4 can be seen at any one time. The remainder can be seen by scrolling through the atlas using the scrollbar on the right side of the window. 9. Because the spectral types represent a sequence of stars at different temperatures, two things can be noticed: • the different spectral types show different absorption lines, and • the overall shape of the continuum changes. The different absorption lines occur because the electrons in different atoms and molecules require different energies to change energy levels. The shape of the continuum is determined by the black body radiation laws. Recall that Wien’s Law states that the wavelength at which the maximum intensity occurs is inversely proportional to the temperature: λmax = 2.9 × 10−3 m · K T (C.1) CHAPTER C. COMPUTER LABORATORIES (CLEA) 51 Using the above information, which of the classified spectra represent the stars with the highest surface temperature? At about which spectral class is the peak continuum intensity at 4200 A˙ (4.200 × 10−7 meters)? What is the surface temperature of this star? 10. Now use the comparison spectra to classify HD 124320. If you look at the classification window, you will see that two known spectra have been drawn, one above and one below the spectrum for HD 124320. You can scroll through the complete set by using the Up and Down buttons on the right side of the window. You should find that this spectrum closely matches that found for the known A1 spectrum. Because all spectral types are not included in the atlas, you will need to do some estimation of your own to determine the exact type (whether it is more like an A1, an A5, or somewhere in between like an A3). 11. You can do this in a more quantitative fashion by using the difference button on the lower right side of the classification window. Selecting this option replaces the lower known spectrum with a graph representing the difference between the upper known spectrum and the unknown. What is your estimate of the spectral type for HD 124320? 12. Record your choice and your reasoning by clicking on Classification Results → Record. Click on Ok to record the data. 13. To determine what atoms or molecules are causing the absorption lines you see, select File → Spectral Line Table. Clicking on any of the listed lines will bring up a red line in the classification window at the position of that line (try for instance 4341). You may also just click on any absorption feature and it will identify the line for you in the list. 14. Now repeat the procedure for the remaining 24 stars in the unknown spectra list (File → Unknown Spectra → Next in List. Record all of your results as before. When you are finished, save the results to a file using Classification Results → Save to File. Please also print your results using the Print choice under the Classification Results menu. You are now going to use the same techniques to identify two unknown stars. You will use a simulated telescope with a photon-counting spectrograph to obtain the spectra and then use that information to help you calculate the distance to the unknown stars. 1. First close the classification window. Then choose File → Run → Take Spectra. First open the dome by clicking on the Dome button, then turn Tracking on so that the telescope rotates at the same rate as the sky. 2. Select any star in your field of view. Center the star in the red square by using the N, S, E, and W buttons (you must hold the buttons down to get significant amounts of movement and not click the 52 CHAPTER C. COMPUTER LABORATORIES (CLEA) buttons). If the telescope is moving too slowly, you may change the rate at which it moves by changing the Slew Rate to a larger value. Once the star is centered, change to the magnified view by clicking Change View. A magnified view of the image in the red square will appear along with two vertical lines. This represents the area the star must be in for the spectrograph to take a spectrum. Again, center the star between the two vertical lines. If you’ve increased the slew rate previously, you may need decrease it now. 3. Once you have positioned the star correctly, click on Take Reading to bring up the spectrograph. Click on Start/Resume Count to start the collection. You will begin to see a trace of the spectrum occurring in real time. In the lower right hand corner of the window you will see a Signal to Noise number. This tells you how strong the signal is compared to the noise in the spectrograph itself and the stray light coming into the spectrograph from sources other than the star you’re observing. You should strive to obtain a signal to noise ratio of at least 10. Once you’ve reached that, click on Stop Count to stop collecting photons. Record some of this data below in Table C.1. Also Save the spectrum. Use the object number in the spectrum window as the object name in the save window. Once you have done that, click Return to the main window, move to a new star and repeat the same process for a second star. Table C.1: Position and Signal to Noise for Unknown Stars Object # Right Ascension Declination Signal to Noise 4. Once you’ve recorded the two spectra, analyze them the same way you did previously. Open the unknown spectra by choosing File → Run → Classify Spectra. Once the classification window appears, you may analyze your spectra by choosing File → Unknown Spectra → Saved Spectra and selecting one of your unknowns. As you classify your spectra, be aware that the stars you observed may not be main sequence stars so you may need to utilize the spectra for giants or supergiants to correctly identify the star. Once you have found the same rough spectral class, choose the luminosity class by choosing Luminosity Near ** and choosing the spectral class that most closely matches what you found by using the main sequence list. Again, these catalogs can be found by choosing File → Atlas of Stellar Spectra. 5. Once you’ve determined the star’s spectral class , choose Classification Results and record your data. Note it will give you the apparent magnitude of the star. Repeat this procedure, recording your data in Table C.2 below. 6. Using the distance-magnitude relation and the tables of absolute magnitudes below, calculate the distance to each star in parsecs and record it in Table C.2. d = 10(m−M+5)/5 (C.2) CHAPTER C. COMPUTER LABORATORIES (CLEA) 53 Table C.2: Unknown Star Spectral Data Star Spectral Type Apparent Magnitude Absolute Magnitude Table C.3: Absolute Magnitudes for Supergiants (I) Spectral Type B0 A0 F0 G0 G5 K0 K5 M0 Absolute Magnitude (M) -6.4 -6.2 -6.0 -6.0 -6.0 -5.0 -5.0 -5.0 Table C.4: Absolute Magnitudes for Giants (III) Spectral Type G0 G5 K0 K5 M0 M5 Absolute Magnitude (M) 1.1 0.7 0.5 -0.2 -0.4 -0.8 Distance (pc) 54 CHAPTER C. COMPUTER LABORATORIES (CLEA) Table C.5: Absolute Magnitudes for Main Sequence (V) stars Spectral Type O5 B0 B5 A0 A5 F0 F5 G0 G5 K0 K5 M0 M5 M8 Absolute Magnitude (M) -5.8 -4.1 -1.1 0.7 2.0 2.6 3.4 4.4 5.1 5.9 7.3 9.0 11.8 16.0 CHAPTER C. COMPUTER LABORATORIES (CLEA) Name: C.2 I. 55 Section: Date: Photoelectric Photometry of the Pleiades Introduction A Hertzsprung-Russell (H-R) diagram is a very important tool in astronomy. It can be used to calculate distances if you know the apparent and absolute magnitude of at least one star. In this lab, you will calculate the distance by comparing two H-R diagrams. The first H-R diagram will be created using the measurements you took of the stars in the Pleiades. You will construct the second H-R diagram from standard data. II. Reference • CLEA Photoelectric Photometry of the Pleiades Lab, http://www.gettysburg.edu/academics/physics/clea/CLEAhome.html • The Cosmic Perspective, Chapter 16, p. 536 – 539 III. Materials Used • CLEA Photometry of the Pleiades program • graph paper • calculator • overhead sheet IV. Activities The observations you will be doing are simulated observations of stars using the CLEA program. You will do the following things in this observation: • measure the brightness of 24 stars using blue and visible wavelength filters, • plot a Hertzsprung-Russell diagram for the Pleiades open cluster, • and use the Pleiades diagram and a standard Hertzsprung-Russell diagram to calculate the distance to the Pleiades. Taking a Dark Frame 1. Start the photometry lab by double-clicking on the Pleiades Photometry icon (Clea pho). 2. Log in to the program by entering all of the group members’ names into the appropriate places after selecting Log In from the File menu. 3. Select Run from the File menu. 4. Open the dome and turn tracking on so that the telescope will track the stars as they move across the sky. 56 CHAPTER C. COMPUTER LABORATORIES (CLEA) 5. Since the instrument will see a surrounding region of the sky in addition to the star you are interested in, we must first take what is known as a dark frame. This will be subtracted from our actual star measurements to reduce our error. 6. Click on the Change View button to switch to the instrument view. Move the telescope until the aperture of the instrument (represented with a red circle) is free of stars. 7. Click on the Take Reading button. Set Seconds to 10 seconds and Integrations to 3. Click Start Count and wait for readings to appear. This was for the visible filter (V). Repeat for the blue (B) filter. Record your mean sky counts in Table C.6 below. Table C.6: Dark Frame Readings Filter Mean sky counts (counts/sec) 8. Once you have obtained readings for each filter, record your data by hitting Record Readings. 9. Return to the main view by clicking Return button and then Change View. Taking Star Readings 1. You will now record the intensities for all of the stars in Table C.7 below. You can move to the correct right ascension and declination by choosing Set Coordinates and entering each star’s coordinates as listed. 2. Press Change View to switch the instrument view. The target star should be centered in the red circle. 3. Choose a filter. You need only take measurements with the B and V filters. 4. Set Seconds to 1.0 second. Then, press Take Reading. Record the apparent magnitudes through both the B and V filters in the table (and on the computer via the Record button). Brighter stars need shorter integration times so feel free to change the number of seconds. Do insure that your signal to noise ratio (S/N ratio) is greater than 100. If the S/N ratio is too low, increase the time 10 or 100 seconds. 5. Calculate B − V for each star and enter it in the appropriate column in Table C.7. 6. You are now done with the computer program. Exit the program and return to the lab room. CHAPTER C. COMPUTER LABORATORIES (CLEA) Table C.7: B and V intensities for Pleiades stars Dec Object Apparent Magnitude (deg m s) Identity B V B–V 24 05 11 1 RA (h m s) 3 41 05 2 3 42 15 24 19 57 3 3 42 33 24 18 55 4 3 42 41 24 28 22 5 3 43 08 24 42 47 6 3 43 08 25 00 46 7 3 43 39 23 28 58 8 3 43 42 23 20 34 9 3 43 56 23 25 46 10 3 44 03 24 25 54 11 3 44 11 24 07 23 12 3 44 19 24 14 16 13 3 44 27 23 57 57 14 3 44 39 23 27 17 15 3 44 39 24 34 47 16 3 44 45 23 24 52 17 3 45 09 24 50 59 18 3 45 27 23 17 57 19 3 45 28 23 53 41 20 3 45 33 24 12 59 21 3 46 26 23 41 11 22 3 46 26 23 49 58 23 3 46 57 24 04 51 24 3 47 29 24 20 34 Star 57 58 CHAPTER C. COMPUTER LABORATORIES (CLEA) Hertzsprung-Russell Diagrams and Distance As we saw in class, the horizontal axis of an H-R diagram is usually labeled by the spectral type or temperature. However, since the color of a star can indicate temperature we can also use B −V on the horizontal axis. For instance, for a hot O-type star, the blue magnitude will be smaller than the visual (yellow) magnitude remember smaller magnitudes indicate greater brightness. For this O-type star, B − V will then be negative. The reverse is true for cool M-type stars. Since the stars in the Pleiades are all part of the same cluster, they are all approximately the same distance from us. With that in mind, we can use the apparent, rather than the absolute magnitude to plot an H-R diagram. 1. On a sheet of graph paper, create an H-R diagram for the stars in the Pleiades. Label the vertical axis with the apparent magnitude through the visual filter (V). The scale for apparent magnitude should run from 25 to 0 (bottom to top). The horizontal axis should be labeled with B − V , with a scale from −0.4 to +1.8. This diagram should take up most of the sheet of graph paper. 2. Plot the Pleiades stars on this H-R diagram and draw a curve through the main sequence stars and label it clearly. Identify any other stars (by luminosity class or type of star) that do not lie on the main sequence. 3. Now plot a second H-R diagram on a plastic overhead sheet for a set of calibration stars given in Table C.8 below. Place the clear sheet over your other diagram and using a ruler trace both the horizontal and vertical axes. Label and scale the horizontal axis exactly as you did for the first diagram. Label the new vertical axis as the absolute magnitude (MV ) through the visible filter. The scale for this axis should run from +17 to −8 (bottom to top). Leave your clear sheet on top of the graph paper so you can use its grid lines. Plot the calibration stars below on the clear sheet’s H-R diagram. Table C.8: Calibration stars for H-R diagram Spectral Absolute Magnitude Type B–V MV O5 −0.35 −5.8 B0 −0.31 −4.1 B5 −0.16 −1.1 A0 0.00 0.7 A5 0.13 2.0 F0 0.27 2.6 F5 0.42 3.4 G0 0.58 4.4 G5 0.70 5.1 K0 0.89 5.9 K5 1.18 7.3 M0 1.45 9.0 M5 1.63 11.8 M8 1.80 16.0 4. Slide the plastic overlay up and down until the main sequence stars from both diagrams lie on top of each other. Since the Pleiades diagram uses apparent magnitude and our calibration star diagram uses absolute magnitude, by sliding the diagrams over each other, we are in effect measuring the difference in apparent and absolute magnitude for any main sequence star in the Pleiades! If we know the difference between the apparent and absolute magnitude, we can calculate the distance in parsecs: d = 10[ m−M +5 5 ] (C.3) CHAPTER C. COMPUTER LABORATORIES (CLEA) 59 Calculate the distance to the Pleiades using any main sequence star and the magnitudes from your H-R diagrams. 5. Convert your distance from parsecs to light years. Recall there are 3.26 light years per parsec. 6. How does your answer compare to the accepted value of 410 light-years? Calculate the percent error between your value and the accepted value. Credit To receive credit on this lab, turn in each student’s data tables and calculations along with a pair H-R diagrams for the whole group. Be sure each group member’s name is on the H-R diagrams. 60 CHAPTER C. COMPUTER LABORATORIES (CLEA) CHAPTER C. COMPUTER LABORATORIES (CLEA) Name: C.3 I. 61 Section: Date: The Hubble Redshift-Distance Relation Introduction In the 1920’s, Edwin Hubble measured the distances of the galaxies for the first time. When he plotted the distance against the velocity for each galaxy, he found that the greater the distance to the galaxy, the greater its speed away from us. In mathematical form, he found recession velocity = H0 × distance, (C.4) where H0 is called the Hubble constant. Astrophysicists readily interpreted Hubble’s relation as evidence of a universal expansion. The distance between all galaxies in the universe is increasing with time. In this lab you are going to find the relationship between the redshift of spectra from distant galaxies and the rate of the expansion of the universe. II. Reference • CLEA The Hubble Redshift-Distance Relation Lab, http://www.gettysburg.edu/academics/physics/clea/CLEAhome.html • The Cosmic Perspective, Chapter 20, p. 636 – 637 III. Materials Used • CLEA Hubble Redshift Distance-Relation program IV. V. • calculator • graph paper Safety and Disposal Activities The observations you will be doing are simulated observations of stars using the CLEA program. You will do the following things in this observation: • Use a simulated spectrometer to acquire spectra and apparent magnitudes. • Determine distances using apparent and absolute magnitudes. • Measure Doppler shifted H and K lines to determine velocities. Using the Hubble Redshift Program ① Open the Hubble Redshift program by double clicking on the Hubble Redshift icon. ② Log in to the program by entering all of the group members’ names into the appropriate places after selecting Log In from the File menu. Click OK when ready. 62 CHAPTER C. COMPUTER LABORATORIES (CLEA) ③ Select Run from the File menu. The screen shows the control panel and view window as found in the “warm room” at the observatory. Open the dome by clicking on the Dome button. Start tracking stars by clicking on the Tracking button. ④ To review the fields of study for tonight’s observing session, select Field from the menu bar at the top of the control panel. The list in the Select star field dialog box contains 5 fields for study. You will need to select one galaxy from each field of view and collect data with the spectrometer (a total of 5 galaxies). ⑤ Choose the first field by clicking on Ursa Major I in the lists of selected galaxies to highlight the field. Then click the OK button. ⑥ Locate the Change View button in the lower left hand portion of the screen. Click on this button to change the view from the finder scope to the instrument. ⑦ User the directional buttons (N, E, S, and W) to move the telescope so that the brightest portion of the galaxy is centered in the spectrometer slit. You may use any galaxy in the field. We will be looking at the spectrum from the galaxy in the slit of the spectrometer. The spectrum of the galaxy will exhibit the characteristic H and K calcium lines which normally appear at wavelengths of 3968.5 ˚ A and 3933.7 ˚ A, respectively, if the galaxies were stationary with respect to us. However, the H and K lines will be redshifted to longer wavelengths. The amount of their shift depends on how fast the galaxy is receding from us. ⑧ To initiate the data collection, press Start/Resume Count from the menu bar in the spectrometer reading window. Continue to collect photons until a clear spectrum of the H and K lines of calcium is displayed. These lines are approximately 40 ˚ A apart. If there is too much noise in the spectrum, you will have to go back and integrate the spectrum to a larger signal-to-noise (S/N) ratio (insure that your signal-to-noise ratio is at least 10). ⑨ Place the cursor in the visible part of the spectrum display and press and hold the left mouse button. The cursor will change from the arrow to a crosshair. Note that displays labeled Wavelength and Intensity now appear at the top of the display. Drag the cursor until the vertical crosshair is centered (as accurately as you can) in the H line, and release the button. Record the measured wavelength for the H line in the Data Sheet below. Repeat the process for the K line. Also, in the Data Sheet, record the galaxy field name and the apparent magnitude. Round numbers to two decimal places. ⑩ Repeat steps ④ to ⑨ for four other galaxy fields. (Ursa Major II has only the K line.) Calculating the Hubble Parameter ① Use your measured magnitudes and the assumed absolute magnitude for each galaxy and derive the distance, D, in parsecs (pc) to each galaxy using the following equation: D = 10( m−M +5 5 ). Then express your answer in megaparsecs (Mpc). Record the distances in the Data Sheet. (C.5) Absolute Magnitude (M) CHAPTER C. COMPUTER LABORATORIES (CLEA) –22 –22 –22 –22 –22 Apparent Magnitude (m) Distance in Mpc Measured H Line (λHmeasured) Measured K Line (λKmeasured) Redshift in H Line (∆λH) Redshift in K Line (∆λK) Velocity for H Line (vH) Velocity for K Line (vK) Average Velocity Figure C.1: Redshifts in the H and K lines for galaxy fields. 63 Galaxy Field Name 64 CHAPTER C. COMPUTER LABORATORIES (CLEA) ② Use your measured wavelengths and the standard wavelengths to calculate the redshifts for each line, ∆λH and ∆λK . ∆λH = λHmeasured − λH , ∆λK = λKmeasured − λK , (C.6) where λH = 3968.47 ˚ Aand λK = 3933.67 ˚ A. Record each on your data table. ③ Use the Doppler shift formula to determine the velocities as determined by both the H and K lines, vH = vK = ∆λH , λH ∆λK c , λK c (C.7) where c is the speed of light, 3.00 × 105 km/s. Calculate the average of the velocities determined from the H and K lines for each galaxy. Record all values in the Data Sheet. ④ Now plot a Hubble diagram by graphing the (average) velocity of a galaxy in km/s vs. the distance in megaparsecs on a sheet of graph paper. Plot the velocity along the vertical axis and the distance along the horizontal axis. Don’t forget to label the axes. ⑤ Draw a straight line through the origin that best fits all the data points. The slope of the line is the Hubble constant H0 . To calculate the slope of the line, measure the distance (D) and the velocity (v) from a point near the upper right end of the line you drew (do not use one of the points that you plotted) and determine H0 using the following equation: H0 = v . D (C.8) Determining the Age of the Universe At the beginning, everything in the universe was at a single point. Since the Big Bang all galaxies are moving away from each other at a more or less constant recession velocity. The Hubble law, Eq. (C.4), can be used to determine the age of the universe. CHAPTER C. COMPUTER LABORATORIES (CLEA) 65 ① Using your measured value of H0 , calculate the recession velocity of a galaxy which is 800 Mpc away. ② Convert 800 Mpc into km. One pc is equal to 3.09 × 1013 km. ③ If we know the distance travelled by the galaxy and the its velocity, we can find the time interval since the galaxy started moving away. time interval = distance travelled . velocity (C.9) Use Eq. (C.9) to find how many seconds ago the universe started. ④ There are about 3.15 × 107 seconds in one year. Convert your answer into years. VI. Credit To receive credit on this lab, you must turn in all of your observations from the CLEA program in the Data Sheet, the plot of the recession velocity vs. distance, and your calculation of the age of the universe. 66 CHAPTER C. COMPUTER LABORATORIES (CLEA) CHAPTER C. COMPUTER LABORATORIES (CLEA) Name: C.4 I. 67 Section: Date: The Period of Rotation of the Sun Introduction Astronomers have been observing sunspots on the surface of the Sun since the time of Galileo. Sunspots turn out to be a useful way of determining the rate of rotation of the Sun. By making direct observations of a sunspot and determining the angular rate they move across the surface at, astronomers can directly calculate the rotational period of the surface of the Sun. II. Reference • CLEA Period of Rotation of the Sun lab , http://www.gettysburg.edu/ academics/physics/clea/CLEAhome.html • 21st Century Astronomy, Chapter 13, p. 339 – 340 III. Materials Used • CLEA Period of Rotation of the Sun program IV. • calculator Observations The observations you will be doing are actual images of the Sun’s surface using the CLEA program. The data you will be using comes from the GONG program ( http://gong.nso.edu/). You will do the following things in this observation: • observe, locate and measure 3 sunspot groups at different latitudes; and • use your observations to determine the rotation rate of the Sun at those latitudes. Observation 1. Start the solar rotation lab. 2. Log in to the program by entering your name into the appropriate place after selecting Log In from the File menu. After logging in, select File → Run. 3. To make measurements, you need to load the images into the program. To begin this process, select File → Image Database → Image Directory → Load. A new window will open, with two columns showing. In the right hand column, will be the list of image files covering a span of 4 months (some days will have multiple images). • Choose a month from which you will choose your observation dates from (January, February, March, or April). • Choose 15 days in that month to get images from (these should be consecutive). 68 CHAPTER C. COMPUTER LABORATORIES (CLEA) • Select an image from each day (attempt to use the same observation time for each image, although this is not critical). • To load images, click on the image name so that it is highlighted, then right click the filename and choose Load. Loaded images will appear in the left hand column. 4. Click on the first image in the left hand column. A new window should move to the front, showing the image for that day. In that window, select Animation → On. This will cycle through the images, giving you a slideshow of your selected images. You should see sunspots move from left to right across the Sun’s surface. After you’ve observed this, you can turn the animation off. 5. Make sure that the displayed image is the first one by clicking on the first image in your list in the left hand column. You will now choose 3 sunspot groups to observe. Pick three different groups that lie at different latitudes on the Sun (remember latitude is the distance north or south of the equator). The sunspots you choose to measure should be anywhere from the center to the left hand side of the Sun. To measure the sunspots, use the procedure below. • Click on your first sunspot group. Two new windows should appear, one with a zoomed in view of the sunspot and a second for you to record the information in. In the window with the zoomed in view (titled “Locate Centroid”), use the scrollbars to center the cursor on the darkest portion of the sunspot. • In the blank field labeled “Spot ID” in the second window, type the letter “A.” When done, hit the Record button. • Repeat this for the 2 other sunspot groups you wish to observe, labeling them “B” and “C” respectively. Your image should now have 3 green squares, with labels, surrounding each of the 3 sunspots you are observing. 6. Click on the next image, repeating the above procedure for each sunspot, labeling appropriately. Repeat this process until you have measured the sunspots in all of your images, or until all 3 spots have disappeared around the edge of the Sun. Finally, before you quit this window, hit Finished. 7. Please print your data file by first selecting, from the main window, File → Measurement Data → Save Data. Then select File → Measurement Data → View/Edit Data. A data window will appear; select List → Print to print your data. You will now analyze your data to determine the rotational period of the Sun. The computer will plot the data and you will use simple controls to obtain a best-fit line through your data points. The slope of this graph will be in degrees/day which you can use to determine the rotational period. 1. In the main window, select Analysis → Plot/Fit Data. 2. In analysis window, select File → Dataset → Load → Longitude Values. A new window will appear - double-click on the row for “A.” The data points will appear on the graph as well as a straight line. Beneath that in the center are some controls which can modify the slope and position of the line. To the left is a readout specifying how good of a fit the line is to the data (RMS) - the goal is to get that as close to zero as possible. To get the best fit use the following procedure. • Make sure that “coarse” adjustments are selected. • Adjust the sliders which control the position and slope of the line until the line gives a fairly good initial fit to the data. • Change “coarse” to “fine” to make the remaining adjustments. • While watching the error, adjust the slope and position such that the error is minimized (ie, you want a value for the RMS that is as small as possible). CHAPTER C. COMPUTER LABORATORIES (CLEA) 69 • When done, select File → Record results. • Right click on the “A” in the graph and choose Remove Dataset. 3. Repeat this process for the data for sunspots “B” and “C.” Close the “Solar Rotation Analysis” window. 4. In this window, select Analysis → Results list. Copy the information from that window into Table C.9. Table C.9: Data for observed sunspots Sunspot Mean latitude Rotation rate A B C V. Calculations You will now calculate the rotational period for the Sun. You will first calculate the rotational period of the Sun, as seen from Earth, using the rotation rate. This period is called the synodic period. Since the Earth is also moving around the Sun as it follows its orbit, the period calculated above is not the period that someone who is at rest with respect to the Sun would measure (like someone looking from another star). You will then calculate the rotational period of the Sun with respect to the stars (the sidereal period). Finally, you will see if there is a difference in rotational period at different latitudes. 1. To calculate the synodic period, remember that in one rotation the Sun will rotate a full 360◦ and you have a rotation rate in degrees/day. Calculate the synodic period for each sunspot and fill in the appropriate spot in Table C.10 2. To convert from synodic period (S) to sidereal period (P), use the equation below. P = S × 365.25 S + 365.25 Record the calculated sidereal periods in Table C.10. 3. Do you notice any trends when comparing rotational periods to latitude from your observed sunspots? If so, describe the relationship between them. 70 CHAPTER C. COMPUTER LABORATORIES (CLEA) Table C.10: Rotational periods for observed sunspots Sunspot Synodic Period (S) Sidereal Period (P) A B C CHAPTER C. COMPUTER LABORATORIES (CLEA) Name: C.5 I. 71 Section: Date: Radio Astronomy of Pulsars Introduction Jocelyn Bell discovered pulsars in late 1967. She was using a new radio telescope to look for short period variations in stellar luminosity in radio wavelengths. She found a new class of objects which became known as pulsars. Pulsars are now known to be neutron stars. Their high rotation rates combine with a strong magnetic field, generate beams of light, primarily at radio wavelengths. When these narrow beams sweep past the Earth, they are seen as a series of rapid, regular pulses. When white light is shone through a prism, a rainbow of light occurs with red light being bent more than blue light. This difference is due to the different frequencies of light. The variation of the speed of light due to frequency is known as dispersion. In materials, different frequencies of light travel different speeds. This is also true of radio wavelengths traveling through the interstellar medium. An individual pulse from a pulsar consists of many frequencies. These different frequencies will travel at different speeds. Astronomers measure the difference in arrival times and use that to calculate the distance to pulsars. In this lab, you will make radio observations of pulsars, measuring at what frequency the pulses are most luminous in, sample the pulse periods, and calculate the distance to two pulsars using dispersion. II. Reference • CLEA Radio Astronomy of Pulsars lab , http://www.gettysburg.edu/ academics/physics/clea/CLEAhome.html • 21st Century Astronomy, Chapter 16, p. 414 – 415 III. Materials Used • CLEA Radio Astronomy of Pulsars program IV. • calculator Observations The observations you will be making are simulated radio observations of a number of pulsars. The simulated observatory uses real data from pulsars to allow you to make these observations. In this lab you will • determine at what frequency pulsars emit most of their energy in; • measure the periods of three different pulsars; and • calculate the distance to two pulsars using dispersion. Observation 1. Start the astronomy of pulsars lab. 2. Log in to the program by entering your name into the appropriate place after selecting Log In from the File menu. After logging in, select File → Run → Radio Telescope. 72 CHAPTER C. COMPUTER LABORATORIES (CLEA) 3. Turn tracking on so that the telescope rotates with the sky. 4. Turn View on to show the sky map (button in lower right hand corner). The yellow dot indicates the position in the sky where the telescope is pointed. 5. There are a number of ways to move the radio telescope: by setting the celestial coordinates, by manually moving the telescope using the N-S-E-W buttons, and using the Hot List menu. For this lab, we will use the hot list. 6. Select pulsar 0628-28 by choosing Hot List → View Select from List → and choosing 0628-28. Click OK and Yes when you are asked if you want to slew the telescope to the selected object. 7. Activate the receiver by clicking Receiver button in upper left hand corner. A new window will appear. This window will show the radio signal being received by the telescope. You can adjust the frequency, vertical gain, and horizontal scale in this window. For now, set the frequency to 400 MHz. 8. Click the Mode button to begin receiving data. Notice the regular peaks showing in the trace. You may adjust the vertical gain while receiving data, but not the horizontal axis. Adjust the vertical gain so that the pulses are as tall as possible, without cutting off the tip of the peak. 9. Click the Mode button again to stop recording. You can only adjust the horizontal scale while not recording. Try various values for the horizontal scale. Notice that as you decrease the horizontal scale size, the signal seems to decrease. This is because the receiver is spending less time collecting data. 10. Reset the horizontal scale to 4 seconds. You can add up to two additional channels to observe at different frequencies by clicking on the Add Channel button. Add two additional receivers. Change the second receiver’s frequency to 800 MHz and the third to 1200 MHz. Insure that all channels have identical horizontal scales and vertical gains. Click on the Mode button to begin receiving data. What do you notice when comparing the three different channels? If you were asked to search for pulsars using a radio telescope, which frequency would you use? 11. Close the second and third channel windows. As pulsars age, their rotation rate slows. This is due to the interaction of the pulsar’s strong magnetic field and surrounding gas and matter surrounding the pulsar. Astronomers can get a good idea of the age of a pulsar by observing the pulse period they receive. Young pulsars generally have the shortest pulse period (this is not necessarily true in cases where the pulsar is part of a binary system). You will now compare the periods of rotation for different pulsars and rank their ages. 1. Rather than measuring the time for a single pulse, it is more accurate to measure a number of pulses and take an average. For your observations, measure the time for 10 pulses and take the average to get the time for a single pulse. 2. You should still have a receiver channel open for pulsar 0628-28. Adjust the horizontal scale so that you can easily see 10 full pulses. Click Mode to get a trace of the signal and then click it again to stop after one complete trace. 3. You can directly measure the time for 10 pulses on the trace. Choose a pulse on the left hand side of the trace. Click and hold the left mouse button. A blue vertical line will appear. You can use the mouse to center this line on your chosen pulse. Release the mouse button when you’ve positioned the line. This represents your zero and the time for this pulse is shown in blue. CHAPTER C. COMPUTER LABORATORIES (CLEA) 73 4. Count over 10 pulses from the blue line. Click and hold the right mouse button and center the white line over the 10th pulse. Release when centered. Record the times shown in the window in Table C.11 below. 5. Repeat this process for the other pulsars shown in Table C.11. You can select new pulsars by using the Hot List in the main window. Pulsar 0628-28 Table C.11: Data for periods of pulsars Start time End time Time for 10 pulses Pulse Period 2154+40 0740-28 0531-21 How do astronomers use dispersion to calculate distance? Consider a real world example. Tyler and Lance have both entered a race, but Tyler can maintain an average speed of 40 km/hr while Lance can maintain 20 km/hr. If both start the race at the same time Tyler will clearly finish first, but the time between when he and Lance finish depends on the length of the race. If the race were 20 kilometers, Lance would finish in an hour while Tyler would finish in half an hour, yielding a difference in arrival time at the finish of half an hour. If the race were 40 kilometers, Lance would finish in two hours while Tyler would finish in an hour, yielding a 1 hour difference in arrival time. The difference in arrival time can be used to determine the distance of the race if you know the average speed for each rider. For both riders the time required to complete a race of length D is given by: t = D v The difference in arrival time is then: tlance − ttyler = = D = D D − vlance vtyler   1 1 − D vlance vtyler tlance − ttyler 1 1 vlance − vtyler (C.10) (C.11) (C.12) Astronomers use a similar process to find the distance to pulsars. In this case, the speeds of the radio waves depend on frequency. Using the laws of physics, astronomers can calculate how the interstellar medium affects the speed of the radio waves: v = f2 , 4150 × ne (C.13) where ne is the number density of electrons in the interstellar medium. From this equation, you should notice that light with high frequencies travels faster than light with low frequencies. In some cases, astronomers cause other techniques to determine the distance to nearby pulsars. Doing so, they can get a measure of ne . 74 CHAPTER C. COMPUTER LABORATORIES (CLEA) From that data, assume the number density of electrons is uniform and equal to 0.03 electrons per cubic centimeter (0.03/cm3 ). This simplifies Eqn. C.13 to: v = f2 124.5 (C.14) In form, the arrival difference for radio waves is the same as it was for Lance and Tyler. We can use the above equation directly, treating Lance as the wave arriving at t2 and Tyler at t1 . D = t2 − t1 1 1 v2 − v1 (C.15) Substituting in the expression for the velocities of the waves from Eqn. C.13: D = t − t1 2 124.5 (f21)2 − 1 (f1 )2  . (C.16) You can now use Eqn. C.16 to calculate the distance to pulsars by measuring the difference in arrival times for different frequencies. The units have been chosen such that you can use the frequencies in MHz. This will result in the distance having units of parsecs. 1. Reset the telescope to point to pulsar 0628-28. 2. In the receiver window, open up three channels and set each to have a vertical gain of 4 and horizontal scale of 4 seconds. Set the frequency for the main channel to 400 MHz, to 420 MHz for the second channel and 440 MHz in the third channel. Click on Mode to receive and then again to stop obtaining data. Notice the delay between the signals (recall that higher frequencies travel faster; ie, it takes longer for the pulses to arrive for lower frequencies). 3. Change the frequencies for the second and third channels to 600 and 800 MHz respectively. 4. Click the Record button in the first channel’s window. Now click on Mode and let 5 complete traces occur (20 seconds). Click Mode again to stop receiving data. Click OK to save the data and click Yes to confirm filename and then OK. 5. Repeat above procedure (steps 3 and 4) for pulsar 2154+40 and one additional pulsar (your choice), making sure to record and save the data each time. You can now analyze your data. Return to the main window and click on File → Run → Data Analysis. A new window will open with the last data file. 1. You can zoom in or out using the zoom buttons or pan left and right using the pan buttons. Adjust the zoom and pan so that you can see two pulses in each of the traces. 2. You can measure the times for each pulse by holding down the left mouse button in each trace. Record those times in Table C.12 below. 3. Load and analyze the other two data files, again recording your data in Table C.12. V. Calculations You will calculate the distance to each pulsar using three different dispersions for each pulsar and averaging the distances to obtain a best-value distance. CHAPTER C. COMPUTER LABORATORIES (CLEA) Table C.12: Data for dispersion of pulsars Pulsar t400 t600 t800 0628-28 2154+40 1. To simplify our calculations, first calculate the difficult part of the denominator for each case. Table C.13: Dispersion values for distance calculations 1 1 1 Frequency 1 Frequency 2 (f11 )2 (f2 )2 (f1 )2 − (f2 )2 600 400 800 400 800 600 2. For each pulsar calculate the distance and then report the average data below each table. Frequency 1 600 Table C.14: Pulsar 0628-28 Frequency 2 t2 − t1 Distance (pc) 400 800 400 800 600 Avg. distance (pc) = 75 76 CHAPTER C. COMPUTER LABORATORIES (CLEA) Frequency 1 600 Table C.15: Pulsar 2154+40 Frequency 2 t2 − t1 Distance (pc) 400 800 400 800 600 Avg. distance (pc) = Frequency 1 600 Table C.16: Pulsar # Frequency 2 t2 − t1 400 800 400 800 600 Distance (pc) Avg. distance (pc) = Chapter D Observations 77 78 CHAPTER D. OBSERVATIONS CHAPTER D. OBSERVATIONS Name: D.1 I. 79 Section: Date: Measuring Angles in the Sky Introduction In this lab you will construct two simple devices for measuring angles and then use these devices to measure the angle between the stars in Orion. You will also take altitude-azimuth data and use that to plot a constellation on graph paper. II. Reference • Lab A.1 III. • meter stick • small weight • protractor • graph paper • index card • scissors • string • compass IV. V. Materials Used Safety and Disposal Activities Measuring angles between two points Probably the simplest device to measure angles between tow objects is the cross-staff. A cross-staff consists of two pieces. The first is the staff. This is a straight length of material which the observer sights along. The second piece, consisting of two vertical marks separated by a known distance, is mounted perpendicular to the sighting rod and is the cross piece. The cross piece’s position along the length of the staff is adjustable. The observer sights down the staff, adjusting the cross piece until the vertical marks are aligned with the two objects of interest. One can then calculate the angle between the objects knowing the distance between the vertical marks on the cross piece and the distance from the observer’s eye to the cross piece. In this lab we will use a meter stick as the staff and an index card to construct our cross piece. 1. To construct the cross piece the index card must be modified: it must have a hole through which it can be placed on the meter stick and two sets of notches cut into it. The two sets (one narrow, one wide) will give you the ability to measure a larger range of angles. • Cut a hole slightly larger than the size of the meter stick centered from left to right and approximately 2 cm above the bottom of the card. • Cut a pair of notches, approximately 5 mm deep, separated by 3 cm, again centered left to right on the card. • Finally, cut a pair of notches separated by 10 cm centered left to right on the card. See Fig. D.1 for an example of the completed cross piece. 80 CHAPTER D. OBSERVATIONS 3 cm 10 cm Figure D.1: Index card cross piece. 2. It is often easier to make observations if we can minimize the reflected light. If you find you are having trouble you can color the entire card black except for narrow bands surrounding the notches in the card. 3. Go outside and use your cross-staff to measure angles. You can try measuring the angle between stars or planets if you know their names, the angle between windows, or something of your own choosing. Record your data in the table (Table D.1) below. Note that you will need to use the smaller gap size to see things which are separated by a relatively small angle. Make sure to use each gap size at least once when making your measurements. Table D.1: Data for angular measurements Object(s) measured Gap used Location of crosspiece (cm) Angle 4. You can read off the angles by using the following graph in Fig. D.2 which plots angle versus the location of the cross piece on the meter stick. Measuring the altitude of objects Previously in the in-class activity Celestial Coordinates you learned about the different coordinate systems used to measure positions of objects in the sky. One of these systems was the altitude-azimuth system. Recall that the altitude is the angle of an object with respect to the horizon. In this portion of the lab you will build a device called an astrolabe and use it to measure the altitude of various objects. Astrolabes similar to what you construct were used by the marine explorers of the fourteenth and fifteenth centuries to help them find their way across the oceans. CHAPTER D. OBSERVATIONS 81 Cross-Staff Conversion Angle vs. Distance 30 Angle (°) 20 10 cm gap 10 3 cm gap 0 20 40 60 80 Position of cross piece (cm) 100 Figure D.2: Graph showing angle as a function of cross piece distance 82 CHAPTER D. OBSERVATIONS 1. Using tape, attach a protractor to a meter stick so that the flat edge of the protractor is parallel to the long edge of the meter stick. See Fig. D.3 below. Figure D.3: Completed astrolabe 2. Attach a string using a stick pin to your apparatus. The stick pin should go through the hole in the center of the flat edge of the protractor. 3. Tie a small weight to the string. 4. To find the altitude of an object, sight along the length of the meter stick with the protractor held perpendicular to the ground. The string should be able to swing freely. Note that due to the way the protractor was attached the angle that you will read off is actually 90◦ - altitude. 5. Again, go outside and use your apparatus to measure the altitude of a number of objects. Record your data in the table below (Table D.2). Table D.2: Altitude measurement data Object observed Altitude CHAPTER D. OBSERVATIONS 83 Measuring the angles in Orion You will use your cross-staff and astrolabe to measure the angles between the stars of Orion and use them to recreate the shape of Orion on paper. 1. Draw a quick sketch of Orion as it appears in the sky below. Label the stars at four corners from 1 to 4. 2. You will need to measure the altitudes of the stars using the astrolabe. Record these values in Table D.3. Table D.3: Altitudes of stars in Orion Star Altitude 1 2 3 4 3. Using your cross-staff you will need to record the angles between the stars. In order to accurately plot the stars in the constellation, for each star you will need to know the angle to at least two other stars (the more you have the better). Carefully measure the angles between the stars and record them in Table D.4. 4. You will recreate Orion on paper using your angle data. The first step is to choose a scale (1◦ = 1 cm) will give a reasonable size. Take a blank sheet of paper and place it so that the long edge is horizontal. Note that the bottom edge of the paper cannot represent the horizon - if it did the constellation would not fit on the sheet of paper. Choose the lower edge to represent an altitude a few degrees below the lowest altitude you measured. 5. Plot the lowest star on the sheet of paper using its altitude, placing it appropriately left and right to insure that the whole constellation will fit on the sheet of paper. 6. Using the compass and your table of data, plot a second star. Do this by using that star’s altitude and the angle it makes to the second star - the compass should be set to a radius (in cm) which represents the angle using your chosen scale. For the scale above, the radius of the compass should be set to the same numerical value as the angle. Place the pin of the compass on the first star and draw an 84 CHAPTER D. OBSERVATIONS Table D.4: Angles between stars in Orion Star pair Gap used Location of cross-piece (cm) Angle between stars 1&2 1&3 1&4 2&3 2&4 3&4 arc across the line which represents the second star’s altitude. Where the arc crosses the line is the location of the second star. See Fig. D.4 below. 7. Plot the positions of the remaining stars. To do this, start with the two stars you’ve already plotted and use the angles between them and a third star. Set the compass to the appropriate size and construct arcs from each of the first two stars; the intersection point will be the location of the third star. Continue this process until all of the stars have been located. It is also helpful to check the stars’ locations against the altitudes you measured earlier. Again, see Fig. D.4 below. CHAPTER D. OBSERVATIONS 85 Location of third star 2 Altitude of second star Altitude of first star 1 Edge of paper (horizon) Figure D.4: Example of finding star locations. VI. Questions 1. Do you think the procedure you used to map Orion could be extended to making a map of the entire sky? Explain. (hint - consider the case of attempting to make a map of the Earth) VII. Credit To receive credit for this lab, you must turn in all of your raw data from Tables D.1 and D.2 as well as the conversion of the cross piece distance to angle for each of the angle measurements. You must also include the data for the altitudes of the stars in Orion as well as your recreation of the constellation on paper from your data. Finally, you need to also include answers to the above question. 86 CHAPTER D. OBSERVATIONS CHAPTER D. OBSERVATIONS Name: D.2 I. 87 Section: Date: Moon Observation Introduction The Moon is, when its up, the most obvious object in the night sky and the second most obvious object seen during the day (again, when it’s up). There are many unique features on the Moon which you can see with the naked eye such as the maria, the dark lava “seas” and the craters. Through a telescope you can see far more detail and get a better view of the mountain ranges, craters and maria. II. Reference • 21st Century Astronomy, Chapter 6 III. Materials Used • telescope IV. • CCD camera (possible) Observations In this lab you will make an observation of the Moon through a telescope. If possible, you will also take an image of the Moon using a CCD camera and then process that image. Ideally you will make this observation at a time when the Moon is not near the full moon phase. A partially illuminated Moon will give you better contrast and hence better surface detail. Observation ① Point the telescope at the Moon, finding it first in the finder scope, then once it’s centered switching to the main telescope. ② Focus the image and sketch the view of the Moon in the space provided in Figure VI.. Also record all of the information asked for. Be sure to capture as much detail as you can. Drawing a few crates is not sufficient as you will need to use your drawing to identify regions on the Moon. ③ If available, ask your instructor for instructions to use the CCD camera to take an image of the Moon. V. Write-Up Using your sketch of the Moon and a map (a globe is available in the lab room or you can find maps on the web) identify at least 3 features in your sketch. Discuss briefly how these features were formed. VI. Credit To receive credit in this lab, you need to turn in your sketch and write-up. If you obtained an image with the CCD camera, you need to email that to your instructor as well. 88 CHAPTER D. OBSERVATIONS Record of Observation Name: Date: Telescope: Time: Right Ascension (h m s) Declination (◦ ’ ”) Magnification: Eyepiece: Observing Conditions: Comments: CHAPTER D. OBSERVATIONS Name: D.3 I. 89 Section: Date: Constellation Quiz: Get To Know Your Night Sky! Introduction There are 88 constellations in the sky. From Radford you can see 48 of them. However, due to the revolution of the Earth around the Sun, visible constellations depend on the time of the year. For example, fall constellations, such as Pegasus, occupy most of the sky in the fall. The celestial sphere and thus constellations slowly rotate toward the west by about 1◦ a day as the Earth orbits around the Sun. In this activity your familiarity with the fall constellations and celestial objects are tested. II. Reference • 21st Century Astronomy, Appendix A-19 – 24. III. Activities Become familiar with the following constellations (and celestial objects within them) that you can find in the sky in the fall. Fig. D.5 might be useful. If you still have trouble identifying the objects in the sky, ask your instructor for help. Constellations • Sirius(Canis Major) • Taurus • Procyon (Canis Minor) • Orion • Castor (Gemini) • Canis Major • Pollux (Gemini) • Canis Minor • Capella (Auriga) • Gemini • Regulus (Leo) • Auriga • Arcturus (Bootes) • Leo • Spica (Virgo) • Bootes • Polaris (Ursa Minor) • Virgo Planets and deep sky objects • Cassiopeia • Saturn • Pleiades (M45) • Orion Nebula (M42) Stars Asterisms • Aldebaran (Taurus) • Big Dipper (Ursa Major) • Betelgeuse (Orion) • Little Dipper (Ursa Minor) • Rigel (Orion) • Winter Triangle (Sirius, Betelgeuse, Procyon) 90 CHAPTER D. OBSERVATIONS You will be asked to find ten of the above constellations, stars, and celestial objects at random during the observation night (when the sky is clear). N Cassiopeia NE Ursa Minor Polaris NW Capella Auriga Ursa Major Bootes Taurus Arcturus E W Castor Pollux Virgo Aldebalan Gemini Rigel Orion Leo Canis Minor Betelgeuse Regulus Procyon Spica Sirius SE Canis Major S Figure D.5: Spring sky in Radford at 8:00 pm on March 1. SW CHAPTER D. OBSERVATIONS Name: D.4 I. 91 Section: Date: Sunspot and Prominence Observation Introduction Sunspots are areas on the Sun which appear darker. We have known about sunspots for hundreds of years, since Galileo first studied them. Sunspots vary in size but are typically about the same diameter as the Earth. Sunspots are related to the Sun’s magnetic field. The magnetic field lines poke out in arcs from one sunspot to the next. When these magnetic field lines “break”, the hot gas flowing along these field lines is expelled away from the Sun. In extreme cases, these can become solar flares. Large solar flares can wreak havoc on the Earth including knocking out power transformers (and then whole power grids) and causing damage to satellites in orbit around the Earth. This project will be worth 3 lab grades (30 points) and will take a maximum of 6 hours (per person) to complete. Each observation only takes 10 - 15 minutes however. II. Reference • 21st Century Astronomy, chap. 1, pp. 343 - 350 III. Materials Used • telescope • hydrogen alpha filter • solar filter IV. Observations In this lab, you will observe the Sun over a period of 2 months, making at least 15 observations of the Sun over this period. During each observation you will make a map of the Sun and plot the position of visible sunspots. In addition, you will sketch any visible prominences using a hydrogen alpha filter. You can look at the Sun directly through the telescope by utilizing a solar filter which blocks most of the light from entering the telescope. Observation of sunspots 1. Place the solar filter on the telescope. 2. Point the telescope at the Sun and insure that it fills the eyepiece. When looking through the eyepiece, cover the finder scope to prevent any accidental burning of the skin as the sunlight will be quite intense after passing through the finder scope. The easiest way to do this is to cover it with a small rag (found with the solar filter). 3. Carefully sketch the Sun, paying careful attention to detail in the position and shape of the sunspots that are visible, in the provided observation sheets Figs. VI. – VI.. 4. Repeat this observation at least 14 more times within a 2 month period. 92 CHAPTER D. OBSERVATIONS Observation of solar prominences 1. Remove the solar filter and replace it with the hydrogen alpha filter. Consult your instructor while doing this! 2. Adjust the position of the telescope until the edge of the Sun is in view. Pan around and look for any obvious prominences. Sketch the prominence, labeling it with the date and time. If time permits, wait 10 - 20 minutes and see if you can see any changes in the prominence. If so, note them on your observation (and resketch). Repeat this observation at least 14 more times within a 2 month period. V. Write-Up Your group must turn in all of your obsevations. Each group member must make at least 4 observations, but may need to make more if you have fewer than 4 members to complete the 15 observations. All observations must contain the date and time of observation as well as well as the name of the observer. Finally, your group must answer the questions below. VI. Questions 1. Do subsequent observations show movement of the sunspots across the surface of the Sun or do they appear to be stationary? If you notice movement, describe the direction and whether all of the sunspots appear to move at the same rate. 2. Did any of the sunspots you observed reappear on the opposite side? If so, determine a rough period for the Sun’s rotation from these observations. 3. Do the sunspots appear to be equally distributed over the surface of the Sun? If not, where do the sunspots appear more prevalent? 4. What is the typical temperature of gases in a prominence? How tall is a typical prominence? 5. At what wavelength does the hydrogen alpha filter work? What is the blackbody temperature of an object whose emission peaks at this wavelength? CHAPTER D. OBSERVATIONS 93 Record of Observation Name: Date: Telescope: Time: Right Ascension (h m s) Declination (◦ ’ ”) Magnification: Eyepiece: Observing Conditions: Comments: 94 CHAPTER D. OBSERVATIONS Record of Observation Name: Date: Telescope: Time: Right Ascension (h m s) Declination (◦ ’ ”) Magnification: Eyepiece: Observing Conditions: Comments: CHAPTER D. OBSERVATIONS 95 Record of Observation Name: Date: Telescope: Time: Right Ascension (h m s) Declination (◦ ’ ”) Magnification: Eyepiece: Observing Conditions: Comments: 96 CHAPTER D. OBSERVATIONS CHAPTER D. OBSERVATIONS 97 Name: D.5 I. Section: Date: Observation With A Telescope Introduction Making observations though a telescope is usually the most exciting part of an astronomy lab. It is very exciting to see real light from celestial objects thousands, and sometimes millions, of light years from us. In this lab you will learn how to set up and point a telescope to various celestial objects for observation. II. Reference • The Cosmic Perspective, Chapter 7, p. 176 – 183. III. Materials Used • telescope IV. • CCD camera (possible) Observations You are going to make observations of five celestial objects including planets, double stars, clusters, nebulae, and galaxies. A list of objects and their coordinates will be supplied by your instructor. If possible, you will also take an image of these objects using a CCD camera and then process that image. Observation 1. Find a location with unobstructed view of the sky. Avoid city lights. Make sure the ground is firm and more or less level. 2. Set open up the tripod legs as far as they go and place the tripod on the ground. Rotate the tripod so that the polar axis of the mount is aligned toward the celestial pole. Use a magnetic compass or Polaris to find the direction of North. If the ground is not level, adjust the length of the legs so that the base of the wedge is level. 3. Connect a power cable to the mount. Listen for the sound of a motor drive in the mount to insure you have a good connection. 4. Loosen the clamps that hold the telescope in position and aim the telescope in the general direction of the object that you are interested in. Tighten the clamps slightly, but not all the way, so that the telescope won’t rotate by itself. Look through the finder scope and use the fine controls to place the object at the center of the cross-hairs. 5. Insert a long-focal length (i.e., low magnification) eyepiece in the eyepiece sleeve. Use the fine control to find the object in the view and place it in the center. Ask your instructor for help is you cannot find the object. 6. Focus the image by turning the focusing nob. If you want, switch to a shorter-focal length (i.e., higher magnification) eyepiece. The magnification of the telescope is given by magnification = focal length of the telescope . focal length of the eyepiece 98 CHAPTER D. OBSERVATIONS 7. Sketch the view of the object (to scale) in the space provided on an observation sheet. Also record all of the information asked for. Be sure to capture as much detail in the object as you can. In addition, if you can observe colors (or other features which are difficult to sketch), note these under Details. 8. If available, ask your instructor for instructions to use the CCD camera to take an image of the object. V. Write-Up Use Starry Night Backyard (in the computer room) to write a very short paragraph about each type of object you have observed. For example, if you observe M31 and M81 which are both galaxies, you must write a paragraph describing what galaxies are. Things that might be covered in these paragraphs are whether or not these objects are in our galaxy, their distances from the Sun, and their approximate ages. If you have any questions, ask your lab instructor. CHAPTER D. OBSERVATIONS 99 Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) 100 CHAPTER D. OBSERVATIONS Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) CHAPTER D. OBSERVATIONS 101 Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) 102 CHAPTER D. OBSERVATIONS Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) CHAPTER D. OBSERVATIONS D.6 I. 103 Moon Journal Introduction The best strategy for learning astronomy at all levels is to begin with observations whenever possible. These provide the basis for introducing the theories that we find in our textbook. They are also crucial in developing an understanding of the concepts rather than simply memorizing terminology. Because of the nature of these observations, they must be made over an extended period of time. The total amount of time involved is approximately a maximum of 6 hours (per person), but the observations need to be spaced out in time; they cannot be done the day before this assignment is due! You are also not allowed to use any resource other than your observations as data. This project is worth 3 lab grades (30 points). II. Materials Used • calendar III. Observation of the Moon What causes the phases of the Moon? Is it possible to predict when and where you will see a specific phase of the Moon? Construct a calendar similar to the one shown below. Whenever you go outside, look for the Moon. Don’t forget that you can often see the Moon in the daytime, too. Whenever you see the Moon, record the following information on your calendar: • Draw a circle for the Moon and shade the dark portion which cannot be seen. • Record time of the day. • Record approximate angle between the Moon and the Sun. • Record approximate altitude of the Moon from the horizon. Sun 31 Mon 1 Tue 2 Wed 3 Thu 4 Fri 5 Sat 6 10:30 pm angle = 150° altitude = 60° 11:15 pm angle = 165° altitude = 70° No observation Rain 10 11 12 13 8:50 am angle = 120° altitude = 45° 10:30 am alngle = 100° altitude = 65° 5:00 am angle = 90° altitude = 70° No observation 6:00 pm angle = 100 ° altitude = 25° 7 8:15 pm angle = 160° altitude = 15° 7:10 pm angle = 125° altitude = 35° 8 9 Cloudy Cloudy No observation Figure D.6: Record observations of the Moon in a calendar. 104 CHAPTER D. OBSERVATIONS Try to space your observations evenly if the weather permits. It is also useful to make note of the days when the Moon was not visible in the sky as well as days when the Moon was obscured by clouds. Measuring Angles in the Sky You don’t need an elaborate instrument to measure angles between two points in the sky. All you need is your hand. Extend you arm fully and open your hand. The distance from the tip of your thumb to the tip of your pinkie, with fingers spread, subtends about 20◦ . Figure D.7: You can use different parts of you hand to measure other angles. width of pinkie width of index index to third width of fist index to pinkie thumb to pinkie 1.5◦ 2◦ 5◦ 10◦ 15◦ 20◦ If the angle between the two points is greater than 20◦ , you can slide your hand along the imaginary line connecting the points. The above table is for an average person. Actual angles extended by parts of a hand depends on individuals. If you think your measurements of angles are off, ask your instructor to calibrate you hand. What are we going to do if we cannot see the Moon and the Sun at the same time in the sky? Suppose you observe the Moon in the western sky in the evening. First, find how many hours have past since sunset and multiply that number by 15◦ . This will give you how many degrees below the western horizon the Sun is. To this angle, add the angle between the Moon and the point on the horizon that is due west. For example, if you observe the Moon 20◦ from the west point on the horizon and it has been 2.5 hours since sunset, then, 2.5 × 15◦ + 20◦ = 57.5◦, CHAPTER D. OBSERVATIONS 105 so the angle between the Moon and the Sun is 57.5◦ . If you observe the Moon before sunrise, find how many hours you have until the sunrise and multiply by 15◦ . This will tell you how many degrees below the eastern horizon the Sun is, then measure the angle between the Moon and the east point using your hand. Add these two angles and you have the angle between the Sun and the Moon. If you have any problem measuring angles, please ask your instructor for help. The altitude of the Moon is measured from the horizon toward the Moon along the vertical circle. The altitude is zero on the horizon; it is equal to 90◦ at zenith. IV. Questions 1. Is it important that your Moon observations (i.e., phase and angle between the Sun and Moon) be made from the same location each time? Explain. 2. Does your data exhibit a periodicity? If so, what is the length of the period? 3. When we observed the right-hand half of the Moon illuminated, we say that we have a first-quarter moon. Why? 4. What relationship exists between the shape of the illuminated portion of the Moon and the angle between the Sun and the Moon? What is the angle when the Moon is a new moon? First-quarter? Full moon? Third-quarter? 5. How would your observations (phase and angle between the Sun and Moon) change if you were living in Australia? V. Credit To receive credit for this assignment, present your instructor with observations (i.e., calendar) and answers to the questions above. Your observations must span a period of at least two months and contain minimum of 25 observations of the Moon. 106 CHAPTER D. OBSERVATIONS CHAPTER D. OBSERVATIONS Name: D.7 I. 107 Section: Date: Observation of a Planet Introduction The development of the telescope allowed astronomers to view the heavens as they had never seen them before, showing the craters on the Moon, sunspots on the Sun, the rings of Saturn, the moons of Jupiter and more. However, even before the telescope astronomers had been able to predict the location of the planets in the sky with great precision. In this lab, you will make observations of a planet and plot its motion against the background sky. II. Reference • 21st Century Astronomy, Chapter 4, pp. 94 – 96. III. Materials Used • Starry Night Backyard IV. • cross-staff (see lab D1) Observations Your group will make a plot of the position of a planet over time. The group must make a minimum of 24 observations spread over two months with the naked eye. This observation will be worth 3 lab grades (30 points) and will take a maximum of 6 hours (per person), however, the actual observations will only take a few minutes per night. Observation with the naked eye 1. Each member of the group should make at least 6 observations (for a minimum of 24 observations - a group with fewer than 4 members will have to make more observations to get the minimum number required). 2. After choosing the planet to observe, use Starry Night Backyard to create a map of the background sky upon which to draw your own observations. The field of view should be set at approximately 25◦ and centered on the planet of interest. 3. Make an observation with the naked eye. Ideally, you will use the cross-staff to measure the angles. You can however use your fist and fingers to make a fairly accurate observation if you do not have your cross staff with you. Measure the planet’s position relative to three background stars. By doing so, you can triangulate the position of the planet. Your fist is approximately 10◦ across when held at arm’s length, therefore each finger is approximately 2.5◦ . Record the angular separations between the planet and three background stars. 4. You can calibrate your printed map by comparing the width of the image in the long direction to 25◦ . This will give you a rough conversion between degrees and centimeters. For example, if the width of your image was 12.5 cm, then there are 2◦ per centimeter. 108 CHAPTER D. OBSERVATIONS 5. Convert your angular measurements from your background stars into centimeters. Assume one of the values you obtained was 8◦ from a particular background star. This converts to a length of 4 cm in the above scale. Set the compass to 4 cm, place the pointed end on the background star, and make an arc. Repeat this process for the remaining measurements. Where the three arcs cross should be the location of the planet. V. Write-Up For those doing naked eye observations, you must include all of your observational data (times, angles to background stars, etc) as well as the completed map of all of your positions over the observation period. Also, include a short write-up concerning the motion of the chosen planet, for instance is the planet moving in a prograde or retrograde direction? Compare your observational path with that shown by Starry Night Backyard. Comment on any differences. CHAPTER D. OBSERVATIONS Name: D.8 I. 109 Section: Date: Observation of Deep Sky Objects Introduction The development of the telescope allowed astronomers to view the heavens as they had never seen them before showing many deep sky objects that originally astronomers thought were “nebulae” in our own galaxy. Some of these objects did turn out to be in our galaxy, but Edwin Hubble was able to show that many of these objects were galaxies outside of our own solar system. Previous to this, many of these objects had been catalogued. The most famous of these catalogs is the Messier catalog which lists over 100 objects found in the night sky. For this observing project, you will observe a minimum of 12 deep sky objects. II. Reference • 21st Century Astronomy, Chapter 4, pp. 94 – 96. III. Materials Used • telescope IV. • CCD camera Observations You will need to make observations of at least 12 different deep sky objects using a telescope and CCD camera. The images taken with the CCD camera will need to be processed to obtain the best images possible. This is especially important for deep sky objects as they are often dim and cover a large angular field. This project will be worth 3 lab grades (30 points) because it will take a maximum of 6 hours (per person). You cannot wait until the last week to make observations and expect to get more than 10 points out of 30. Observation with a telescope There are a number of telescopes that can be used for this observation project. You should schedule a time for an initial observation with the instructor to give you instruction on setup and use of the equipment. After this first observation, you will just need to schedule a time to check out the equipment to make observations. Below is the method for setting up the Celestron GPS-guided 8” telescope. If you are using another telescope, consult with your instructor on the procedure for aligning and using the telescope. 1. Carefully carry the telescope out to the observing site. The site should be as clear as possible of trees and other items which may block your view. You will also need to wheel out the astronomy cart with the computer and CCD camera setup on it. 2. Run a power cord (or series of power cords) to the observation site. Plug in the computer and start it up. 3. Release the altitude lock on the telescope (left hand side). Adjust telescope so that it is in a horizontal position. This can be easily accomplished by lining up the silver lines on the left hand side of the mount. When aligned, re-engage the altitude lock. 110 CHAPTER D. OBSERVATIONS 4. Carefully remove the end caps from the telescope and finder scope. 5. Connect the power adapter to the telescope and turn the telescope on (power switch is next to the adapter plug-in). Grab the handset on the right fork mount. Follow the instructions to obtain a GPS alignment (ie, hit “Align”). The telescope will now slew around in azimuth to find north. Once there, it will slew to the first alignment star (typically Arcturus in the early fall). When the telescope stops moving, look through the finder scope and insure that the brightest star (Arcturus for instance) is on the cross-hairs. If it is not, take a quick check through the eyepiece to insure that the finder scope’s alignment has not been jostled. If Arcturus is visible in the eyepiece, but is not centered in the finder scope, consult your instructor to get the finder scope re-aligned. 6. Is the bright star centered in the eyepiece? If not, adjust its position by using the four directional arrows on the handset. When it is centered, follow the instructions on the handset to the second alignment star. The alignment procedure with the second star follows the identical procedure as the first. 7. During the above process, someone should login to the computer. Start up CCDOPS from Start → Programs → CCDOPS. 8. Begin the process of cooling the CCD by setting the temperature to −5◦ . If it is a cool and dry night out, you can set it lower. However this risks dew forming on the camera due to its cold temperature. If in doubt, ask your instructor. 9. Remove the current eyepiece and replace it with the iFocus eyepiece. Carefully focus the telescope on the second alignment star, taking time to let the telescope adjust as the focus will vary due to vibrations from your contact in addition to atmospheric movement. If the star is not visible in the iFocus eyepiece, re-insert the original eyepiece and insure that the second alignment star is very close to dead center. Once completed, continue focus process with the iFocus eyepiece. 10. Remove the iFocus eyepiece carefully without hitting the focus knob. Replace it with the CCD camera, tightening the screws down to insure the camera is stable. 11. Using CCDOPs, take an image of the star and insure that is in focus. If it is not, slowly adjust the focus until the star is in focus. From this point on do not adjust the focus! If you touch the focus knob, you will need to refocus the telescope for the CCD camera. 12. Once the camera is focused, you can now tell the telescope to point to the desired object. For instance, if you wanted to look at a Messier object, use the telescope handset. Hit “1” and enter the number of the desired Messier object, then hit “Enter.” The telescope should slew to the object. Check through the eyepiece that the object is centered. If it is not, adjust the telescope using the directional arrows so that the object is centered in the eyepiece. Depending on the atmospheric conditions and ambient light pollution, it will almost certainly be better to take many very short duration images rather than one longer exposure time. You may choose to take either color or black and white images. You can always process the images later to increase contrast or color balance. 13. Save your images as a FITS file using the following naming format: lab section-object name-date-group name.fits where the date should be in mmddyy format. It will be easiest if you create your own folder in which you will save all of your images. Also be sure to record the name of the person/people making the observation in the notes. 14. If you are the last group to use the telescope that evening, return all items back to the lab room. 15. After collecting your images, consult your instructor on the method of processing the images. CHAPTER D. OBSERVATIONS V. 111 Write-Up You must include all of your observational CCD files (I will pull those directly from the computer - you must tell me which directory they are in). This includes pre-processed and post-processed images. You must include a short write up about the name and type of object for each object observed. This does not have to be in great detail. Most of your effort will be spent in obtaining and processing images. 112 CHAPTER D. OBSERVATIONS CHAPTER D. OBSERVATIONS Name: D.9 I. 113 Section: Date: The Sun and Its Shadow Introduction Although one may not think of making astronomical observation in the daytime, there are a number of activities that one can undertake in broad daylight. Those include observations of the Sun and Moon. In this exercise, we will study the motion of the Sun by looking at the shadow of a vertical pencil and its changing rising and setting location. This lab will be worth 3 lab grades (30 points) and will take a maximum of 6 hours (per person). II. Reference • 21st Century Astronomy, Chapter 2, pp. 9 – 14. III. Materials Used • large piece of cardboard • marking pen • large sheet of paper • watch or clock • pencil • protractor • piece of clay • magnetic compass IV. Safety and Disposal Do not directly look at the Sun. V. Observations of the Sun’s Shadow You will need to make multiple observations of the Sun throughout the day and at different times of the semester. These observations must be made at the same location each time. It is recommended that the observations for measuring the Sun’s shadow be spaced at least two or three week intervals. The observations of the Sun’s rising and setting location must be done from the same location as well, though not necessarily the same as that used for measuring the Sun’s shadow. Sun’s shadow In this portion of your project, you will observe the changing length of the shadow cast by a simple sundial over the course of a day. Your group must have a total of four of these measurements over the semester, preferably one from each group member. To record the Sun’s shadow, you will create a simple sundial as shown below. 1. Tape the sheet of paper on the cardboard. 2. Place the cardboard where it will receive sunlight during the majority of the day. 3. At the middle of the sheet of paper, place an ×. 114 CHAPTER D. OBSERVATIONS 4. Using a magnetic compass orient the cardboard so that the longer side of the sheet is aligned with the East-West line. After leveling the cardboard, draw a straight line from the base of the pencil to due North using the compass. This is the magnetic North-South line. 5. Stand a pencil vertically using a piece of clay centered on the ×. The pointed end of the pencil must be pointing up. Once standing, record the height from the paper to the tip of the pencil somewhere on the sheet of paper. Sun E N bo Card 10:07 8:59 8:02 ard S 7:05 W Sh eet Figure D.8: Tracing the Sun’s shadow. 6. Mark the tip of the shadow of the pencil at approximately hourly intervals during the day. Make more frequent observations, if possible, during the middle of the day. Be sure to record the time of each observation. 7. When you are finished, draw a smooth curve going through your observation points on the sheet. Determining local noon You can use your observation to determine the relationship between local noon and clock time. Local noon is the time when the Sun is due south and transiting your local celestial meridian. It is at this time, that the Sun reaches its maximum altitude. 1. What does this say about the length of the shadow of the pencil at the local noon? Note that the variation in the length of the shadow near noon is quite small. 2. How can you determine the shortest shadow? There are several ways of doing this; some are more accurate than others. Find the one that you think gives a reasonably accurate answer. CHAPTER D. OBSERVATIONS 115 3. How do you account for the difference between the local noon obtained from the shadow and the noon of the Eastern Standard Time? Finding geographic north You can find the direction of geographic North using your observation. , that is, the direction of your local line of longitude from using your observation. 1. Find the point on the curve you drew on the sheet closest to the base of the pencil. Draw a line between this point and the × at the center of the sheet. 2. Measure and record the angle between this line and the magnetic North-South line using a protractor. 3. Why do the geographic and magnetic North-South lines point in different directions? VI. Observations of the Sun’s Rising and Setting Location In this portion of your project, you will observe the changing position of the Sun’s rising and setting location. All of these observations must take place at the same spot. Observations 1. Choose a location from which all your observations will be made. It must be easily accessible to all members of your group. If a single location will not suffice, part of the group can work at one location and the remainder at a second. If this is the case, one group should do sunrise and the other sunset. 2. Take two photographs, one facing due east and the other due west. A digital photograph will probably work best. Make sure that the image has a large field of view (ie, don’t zoom). You can use a compass to get the directions of due east and west. Mark the location of due east and west on the photographs. 3. Observe the sunrise and sunset. Your group must make a total of 20 observations of both sunset and sunrise (total of 40) spread over a period of 2 months. Mark on the photograph the rise or set location relative to landmarks in the photo. Also record, on a separate sheet, the rise or set time. 116 VII. CHAPTER D. OBSERVATIONS Write-Up Turn in your two photographs, your table of rise and set times, and a minimum of four shadow observations. Write a short (2 pages maximum) report summarizing your data. Include in your report a description of why the rise and set times and positions change over the year as well as a discussion of why the shadow tracings you made differ over time. Finally, make sure that your report answers all of the questions throughout the text of the lab. VIII. Extra credit 1. Using your data from each shadow plot, determine mathematically the maximum altitude the Sun reached for each observation. You will need to use the length of the pencil and the length of the shadow to determine this. Hint - set up a right triangle to find the altitude. CHAPTER D. OBSERVATIONS Name: D.10 I. 117 Section: Date: Object X Introduction In this lab, you will attempt to identify 3 different objects for which you initially know only the celestial coordinates. You may work in groups of two for this lab maximum. While not required, it will be helpful if you have previous experience running the CLEA labs in ASTR 111 (the labs we do in this class during the semester will give you the requisite experience). This lab will be worth 3 lab grades (30 points) and will take a maximum of 6 hours (per person). II. Reference • CLEA Object X lab manual http://www.gettysburg.edu/academics/physics/clea/objectxlab.html III. Materials Used • CLEA Object X lab IV. Object X lab To successfully complete this project, you must correctly identify three unknown objects. To do so, you will need to use all of the tools and your own deductive reasoning to determine what type of object you are observing. Your objects could be asteroids, stars, galaxies, quasars, or pulsars. You may observe your objects with optical and/or radio telescopes. You will have numerous detectors available. Additional information on how to use the telescopes and detectors can be obtained by previous experience with the relevant labs or by consulting with the instructor. The CLEA lab manual will be an excellent resource in addition to help you with your assignment. V. Write-Up For each set of coordinates given to you by the instructor, identify the type of object and the information for each type given below. • Pulsar – period – dispersion – distance • Galaxies – Z (doppler shift) • Stars – visual magnitude (V) – blue visual magnitude (B) 118 CHAPTER D. OBSERVATIONS – B-V – spectral class • Asteriods - will be given observing time in addition – exact position coordinates of asteroid in both “discovery” images • Quasars – Z (doppler shift) and measured wavelengths of spectral lines Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.) Observation Sheet NAME SEC. DATE TIME (indicate UT, EST, EDT, etc.) NAME OF OBJECT COORDINATES R.A. TELESCOPE h m DEC. EYEPIECE ° ' EPOCH mm MAGNIFICATION SEEING (clear, moonlight, haze, calm, moderate, turbulent, thin clouds, etc.)