Transcript
Mon. Not. R. Astron. Soc. 393, 1353–1358 (2009)
doi:10.1111/j.1365-2966.2008.13947.x
Astrometric observations of the Uranian satellites with the Faulkes Telescope North in 2007 September M. Yu. Khovritchev Central Astronomical Observatory of RAS, Pulkovskoye chaussee 65/1, Saint-Petersburg 196140, Russia
Accepted 2008 September 10. Received 2008 July 7; in original form 2008 April 29
ABSTRACT
The results of astrometric observations of the main Uranian satellites taken with the Faulkes Telescope North are presented. A median filter algorithm was applied to subtract a scatteredlight halo caused by Uranus. The Two-Micron All-Sky Survey (2MASS) and USNO-B1.0 were used as reference catalogues. The mean value of the differences between the equatorial coordinates of the satellites determined with 2MASS and USNO-B1.0 is close to 200 mas. A comparison of the observed equatorial coordinates of the satellites and their relative positions with ephemerides based on different combinations of theories of motion of Uranus and its satellites (DE405+GUST86, DE405+GUST06, INPOP+GUST86, INPOP+GUST06) was performed. The satellites’ positions obtained with respect to 2MASS are in better agreement with theories. The values of (O−C) of the equatorial coordinates determined with the 2MASS are mainly less than 100 mas. The majority of (O−C) of relative positions are within ±50 mas. The mean values of the standard errors of (O−C) are within 20 to 60 mas. Key words: astrometry – planets and satellites.
1 I N T RO D U C T I O N The current epoch of the Uranian equinox stimulates observations of the satellites of the planet. The most essential type of observations during this period is observations of mutual occultations and eclipses of the major satellites. Photometric and astrometric observations of these events allow us to obtain very reliable information to improve the theory of motion of the Uranian satellites and to determine their physical parameters (Hidas, Christou & Brown 2007). Moreover, the observations were made to obtain the positions of the satellites in the systems of the modern astrometric catalogues and the mutual relative positions of the satellites take on special significance. These observations are especially useful in cases of close approaches between satellites. Such observations may provide additional data necessary for better understanding of the results of the photometric observations of the mutual events. The long focal length telescopes with CCD cameras that allow us to take CCD images with scales of several tenths of arcsec per pixel have undoubted advantages for astrometric observations of the Uranian satellites. Astrometric reductions of the CCD images taken with these instruments are complicated by insufficient density of coverage of the celestial sphere by stars of accurate astrometric catalogues. They do not provide the necessary number of stars fainter than 16 mag with positional accuracy better than 20 to 80 mas in relatively small fields of view (near to several arcminutes). Hence, the analysis of possible systematic errors of the observed E-mail:
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positions of the Uranian satellites caused by the use of the catalogues of the faint stars within magnitude range 16–20 is required. The results of astrometric observations of the main Uranian satellites (equatorial coordinates and relative positions ‘satellite minus centre of mass of the satellites’ images (sat − cm)’) performed with the Faulkes Telescope North (FTN) in 2007 September are presented in this paper. Section 2 contains detailed information about the observations and data processing. In Section 3 we present the results of the comparison between the observed positions of the main Uranian satellites and the satellites’ positions calculated with the different combinations of the theories of motion of Uranus (DE405, INPOP) and its satellites (GUST86, GUST06) and estimates of standard errors of coordinates of the satellites. Conclusions are discussed in Section 4. 2 O B S E RVAT I O N S A N D DATA R E D U C T I O N CCD images of the main Uranian satellites were taken with the 2.0m FTN on 2007 September 3 and 4, during two remote control sessions via web interface. The FTN was equipped with a 2048 × 2048 E2V CCD42-40 camera. The resulting CCD images were binned 2 × 2 and the pixel scale was 278 mas pixel−1 . A Sloan Digital Sky Survey i filter was applied. A set of nine CCD images was obtained. The exposure time of the CCD images are 2 s (one CCD image), 3 s (one CCD image), 5 s (four CCD images) and 30 s (three CCD images). Only CCD images with exposure times of 5 and 30 s contained stellar images that were able to fit. Equatorial coordinates of the satellites and the relative positions ‘satellite-centre of mass of
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Figure 2. Profiles of the images of the satellites plotted along the mean line of Uranian satellites’ configuration before filtering (top panel) and after filtering (bottom panel).
2003) and Two-Micron All-Sky Survey (2MASS) (Cutri et al. 2003) catalogues. Two UCAC2 stars in one of the sets of CCD images is an insufficient quantity to decide which catalogue is better in the observed field. The values of differences USNO-B1.0−UCAC2 do not strongly differ from the 2MASS−UCAC2 of these stars. Absolute values of the differences in RA and Dec. are within 15 to 215 mas. This does not allow one to adopt the satellites’ positions referred to in USNO-B1.0 or 2MASS as a unique solution. The CCD images contain seven to 18 stars form these catalogues. Astrometric reductions were performed using six constant linear models in the systems of both catalogues separately. The unit weight errors of astrometric reduction based on the 2MASS catalogue data are less than those calculated using the USNO-B1.0 catalogue. These values are within 150–200 mas in the case of the USNO-B1.0 catalogue and 80–150 mas with the 2MASS catalogue.
Figure 1. The images of Uranus and satellites taken on 2007 September 3. The top panel contains the CCD image before median filter application, and the filtered CCD image is seen on the bottom panel.
the satellites images (sat − cm)’ were determined only for these CCD images. The images of Uranus were overexposed, and scattered-light halo deformed the satellites’ images. The most significant influence of the halo was revealed for satellites that were seen relatively close to Uranus. The median filter with a 9 × 9 pixel window was applied to all CCD images to reduce the influence of the halo. The examples of the CCD images, satellite configuration and result of filtering are given in Fig. 1. Fig. 2 demonstrates how the scattered-light halo distorted the profiles of the satellites’ images, and how the median filter procedure allows us to subtract the halo-dependent trend. Images of reference stars and satellites were fitted to obtain their pixel x, y positions. The Lorentzian function was used as a point spread function. Only pixel data within an aperture of radius 7 pixels were used for each object to reduce the effects of interaction of the close images of the satellites. The field of view of the FTN with the E2V CCD42-40 camera is 4.6 arcmin. The magnitudes of the reference stars are within 14 to 18. They are mainly fainter than 16 mag. As a result, there are insufficient images of the reference stars from high precision astrometric catalogues such as UCAC2 (Zacharias et al. 2004) (only two stars in one set of the CCD images). Hence, the positions of the reference stars were taken from the USNO-B1.0 (Monet et al.
3 C O M PA R I S O N W I T H T H E O RY O F M OT I O N The DE405 (Standish 1998) and INPOP (Fienga et al. 2008) theories were used to calculate ephemerides of Uranus. The GUST86 (Laskar & Jacobson 1987) and GUST06 (Emelyanov et al. 2006) theories were applied to compute the satellites’ positions. As a result, the ephemerides of the satellites were calculated from combinations DE405+GUST86, DE405+GUST06, INPOP+GUST86 and INPOP+GUST06. All calculations were performed with the ‘natural satellite service’ (Emelyanov et al. 2006). Equatorial coordinates (RA and Dec.) of the Uranian satellites and appropriate values of the (O−C) for each combination of the C
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Table 1. Equatorial coordinates of the Uranian satellites determined with respect to USNO-B1.0 and (O−C) values calculated with the different theories. The mean values of (O−C) and their standard errors for each satellite are displayed in separate lines. Sat
Date (UTC) (h
U1 U1 U1 U1 U1 U1 U1
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
RA m s)
23 12 50.4845 23 12 50.4958 23 12 42.2281 23 12 42.2020 23 12 42.2155 23 12 42.1866 23 12 42.1919
(◦
Dec.
)
−05 56 21.960 −05 56 21.967 −05 57 42.286 −05 57 42.240 −05 57 42.389 −05 57 42.407 −05 57 42.540
U2 U2 U2 U2 U2 U2
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 51.0251 23 12 51.0339 23 12 41.8744 23 12 41.8418 23 12 41.8267 23 12 41.8320
−05 56 52.068 −05 56 52.082 −05 57 24.227 −05 57 24.034 −05 57 24.279 −05 57 24.344
U3 U3 U3 U3 U3 U3 U3
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 51.1072 23 12 51.1144 23 12 42.5516 23 12 42.5278 23 12 42.5333 23 12 42.5113 23 12 42.5147
−05 56 55.334 −05 56 55.397 −05 58 00.448 −05 58 00.405 −05 58 00.473 −05 58 00.478 −05 58 00.638
U4 U4 U4 U4 U4 U4 U4
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 50.3110 23 12 50.3223 23 12 41.3674 23 12 41.3416 23 12 41.3522 23 12 41.3294 23 12 41.3345
−05 56 14.208 −05 56 14.205 −05 56 56.104 −05 56 55.969 −05 56 56.147 −05 56 56.117 −05 56 56.299
U5 U5
2007 09 03.61656 2007 09 03.61739
23 12 50.5669 23 12 50.5839
−05 56 25.548 −05 56 25.673
All satellites
DE405 GUST86
INPOP GUST06
−384 −106 39 −264 27 −323 −150
93 139 103 197 94 121 38
−380 −101 26 −276 14 −336 −162
97 143 95 188 86 112 30
−291 −12 133 −170 120 −230 −56
215 261 225 319 217 243 160
−286 −7 120 −182 108 −242 −68
219 265 217 310 208 235 152
−166 ±63 −336 −90 −50 −348 −485 −303 −269 ±68 −346 −131 4 −262 −90 −335 −188 −193 ±49
112 ±18 93 116 259 491 265 221 241 ±58 120 117 52 135 106 138 20 98 ±17
−174 ±62 −342 −96 −64 −362 −498 −317 −280 ±68 −331 −115 27 −239 −67 −312 −164 −172 ±50
107 ±19 99 122 274 506 280 236 253 ±60 121 117 65 147 118 151 33 107 ±16
−72 ±63 −242 4 44 −255 −391 −210 −175 ±68 −252 −37 98 −168 4 −241 −94 −99 ±49
234 ±18 215 239 381 613 387 343 363 ±58 242 239 174 257 228 260 142 220 ±17
−80 ±62 −248 −2 30 −268 −404 −223 −186 ±68 −237 −21 121 −146 27 −218 −71 −78 ±50
229 ±19 221 244 396 629 402 358 375 ±60 243 240 187 270 241 273 155 230 ±16
−348 −64 34 −260 −9 −264 −89 −143 ±55 −508 −140
53 89 71 236 89 148 −1 98 ±29 313 233
−348 −64 32 −262 −11 −266 −91 −144 ±55 −500 −132
67 102 80 246 98 158 8 108 ±28 313 233
−254 30 128 −166 84 −170 5 −49 ±55 −414 −46
175 211 193 359 211 270 121 220 ±29 435 355
−254 30 126 −168 82 −172 3 −50 ±55 −406 −38
189 224 202 368 221 280 130 231 ±28 435 355
−199 ±29
143 ±19
−198 ±29
149 ±19
−105 ±29
265 ±19
−104 ±29
271 ±19
theories are presented in Table 1 (with respect to USNO-B1.0) and Table 2 (with respect to 2MASS). The values of the (O−C) distinctly depend on the reference catalogue and theory combination used. The most significant differences between the sets of (O−C) may be caused by Uranus motion theories and differences between catalogues. The influence of the theory of Uranus motion is revealed as differences between (O-C) of appropriate sets that are near to 100 mas on average. The distinction between the satellites’ ephemerides (GUST86 and GUST06) is detected at several mas levels. On the whole, the absolute values of (O−C) calculated with satellites’ positions referred to in USNO-B1.0 are greater than the same values computed using satellites’ coordinates determined with respect to 2MASS. The mean value of the differences between the equatorial coordinates of the satellites determined with 2MASS and USNO-B1.0 is close to
C
(O−C)RA and (O−C)Dec. , mas DE405 INPOP GUST06 GUST86
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200 mas. The mean values of standard errors of the (O−C) results are within 20 to 60 mas for both catalogues. The positions of the satellites (X,Y) with respect to the centre of mass of the images of all satellites presented on each CCD image sat − cm were determined with both reference catalogues. Table 3 contains these relative positions of the satellites and (O−C) of X,Y computed with GUST86 and GUST06 theories. The differences between (O−C) of different sets of sat − cm positions depend on the catalogue used. They are significantly less than the similar differences in the case of the equatorial coordinates. In most cases, they are less than several tens of mas. In addition, equatorial coordinates of Uranus were deduced from equatorial coordinates of the satellites with respect to USNO-B1.0 and 2MASS and satellites’ ephemerides GUST86 and GUST06. The results are presented in Table 4.
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Table 2. Equatorial coordinates of the Uranian satellites determined with respect to 2MASS and (O−C) values calculated with different theories. The mean values of (O−C) and their standard errors for each satellite are displayed in separate lines. Sat
U1 U1 U1 U1 U1 U1 U1
Date (UTC)
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
RA (h m s) 23 12 50.5034 23 12 50.5086 23 12 42.2313 23 12 42.2172 23 12 42.2181 23 12 42.2130 23 12 42.1988
(◦
Dec.
)
DE405 GUST86
−05 56 22.153 −05 56 22.071 −05 57 42.493 −05 57 42.529 −05 57 42.605 −05 57 42.490 −05 57 42.670
U2 U2 U2 U2 U2 U2
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 51.0479 23 12 51.0497 23 12 41.8749 23 12 41.8619 23 12 41.8583 23 12 41.8436
−05 56 52.235 −05 56 52.162 −05 57 24.482 −05 57 24.394 −05 57 24.372 −05 57 24.615
U3 U3 U3 U3 U3 U3 U3
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 51.1305 23 12 51.1305 23 12 42.5548 23 12 42.5425 23 12 42.5357 23 12 42.5363 23 12 42.5231
−05 56 55.499 −05 56 55.475 −05 58 00.632 −05 58 00.652 −05 58 00.667 −05 58 00.548 −05 58 00.762
U4 U4 U4 U4 U4 U4 U4
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 50.3288 23 12 50.3342 23 12 41.3715 23 12 41.3571 23 12 41.3589 23 12 41.3604 23 12 41.3392
−05 56 14.408 −05 56 14.316 −05 56 56.377 −05 56 56.370 −05 56 56.413 −05 56 56.211 −05 56 56.469
U5 U5
2007 09 03.61656 2007 09 03.61739
23 12 50.5863 23 12 50.5971
−05 56 25.739 −05 56 25.774
All satellites
The results of the comparison of the deduced Uranus position with ephemerides DE405 and INPOP are also shown in Table 4. These results inherit the influences of the reference catalogues and theories that are seen in previous calculations.
(O−C)RA and (O−C)Dec. , mas DE405 INPOP GUST06 GUST86
INPOP GUST06
−101 86 87 −36 66 73 −46
−100 35 −104 −92 −122 38 −92
−96 91 74 −48 53 60 −59
−96 39 −112 −101 −130 30 −100
−7 180 181 58 159 166 48
22 157 18 30 1 160 30
−2 185 168 46 147 154 35
26 161 10 21 −8 152 22
18 ±29 6 147 −43 −47 −11 −129 −13 ±37 3 110 52 −42 −54 40 −62 7 ±24
−62 ±26 −74 36 4 131 172 −50 37 ±40 −45 39 −132 −112 −88 68 −104
11 ±29 0 141 −56 −61 −24 −143 −24 ±38 19 126 75 −19 −31 63 −38
−67 ±27 −68 42 19 146 187 −35 49 ±41 −44 39 −119 −100 −76 81 −91
112 ±29 100 240 51 47 83 −36 81 ±37 97 204 146 52 40 134 32
60 ±26 48 159 126 253 294 72 159 ±40 78 161 −10 10 34 190 18
105 ±29 94 235 37 33 70 −49 70 ±38 113 220 169 75 63 157 55
55 ±27 54 164 142 269 309 87 171 ±41 78 162 3 22 47 203 31
−53 ±30
28 ±24
−44 ±29
101 ±24
69 ±30
122 ±24
78 ±29
−81 114 96 −27 91 201 −18 54 ±37 −217 58
−147 −22 −202 −164 −177 54 −171 −119 ±36 122 132
−81 115 94 −29 89 199 −21 52 ±37 −209 66
−133 −9 −193 −155 −168 64 −162 −108 ±36 122 132
13 208 190 66 185 295 75 148 ±37 −124 152
−25 100 −80 −42 −55 176 −49 3 ±36 244 254
13 208 188 64 183 293 73 146 ±37 −115 160
−11 114 −71 −33 −45 186 −40 14 ±36 244 254
11 ±17
−40 ±19
12 ±17
−34 ±20
105 ±17
82 ±19
106 ±17
88 ±20
The mean values of the (O−C) in equatorial coordinates depend on reference catalogue and Uranus motion theory. Cataloguedependent differences between (O−C) are close to 200 mas. The satellites’ positions obtained with respect to 2MASS are in better agreement with theories than the coordinates of the satellites determined with respect to USNO-B1.0. The effect in (O−C) caused by the theories of Uranus motion is about 100 mas. The influence of Uranian satellites’ theories on (O−C) values is less than 10 mas on average. The catalogue-dependent differences between (O−C) values may be caused by a common shift of positions of all reference stars between 2MASS and USNO-B1.0 within the field of view. The mean differences of the positions of the reference stars are 270 and −210 mas in RA and Dec., correspondingly. These values are in good agreement with the mean differences between (O−C)
4 CONCLUSIONS The results of astrometric observations of the main Uranian satellites taken with the FTN are presented in this paper. It includes positions of the satellites referred to the USNO-B1.0 and 2MASS catalogues (RA, Dec.), relative positions sat − cm and the results of calculation of the (O−C) values with two theories of Uranus motion (DE405 and INPOP) and two ephemerides of the Uranian satellites (GUST86 and GUST06).
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Table 3. Positions of satellites (X,Y) calculated with respect to centre of mass of the satellites images (sat − cm) and (O−C) values calculated with the GUST86 and GUST06 theories. The mean values of (O−C) and their standard errors for each pair of the satellites are displayed in separate lines. USNO-B1.0 Sat
Date (UTC)
X
Y
2MASS (O−C)
x
y
(arcsec)
x
U2 U2 U2 U2 U2 U2 U2
2007 09 03.61656 −3.1993 11.8636 2007 09 03.61739 −3.1966 11.8978 2007 09 04.60648 3.3228 −11.5198 2007 09 04.60783 3.4284 −11.6282 2007 09 04.60716 3.3363 −11.5552 2007 09 04.60847 3.3284 −11.5868 2007 09 04.60919 3.3363 −11.5847
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
4.8661 −18.2444 4.8315 −18.2172 −1.9540 6.5393 −2.0331 6.5598 −2.1468 6.7268 −2.0409 6.5412 −2.0331 6.6113
U3 U3 U3 U3 U3 U3 U3
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
6.0910 6.0325 8.1491 8.1968 8.1696 8.1726 8.1521
−21.5104 −21.5322 −29.6818 −29.7203 −29.7123 −29.6578 −29.6827
U4 U4 U4 U4 U4 U4 U4
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
−5.7878 −5.7851 −9.5179 −9.5000 −9.4512 −9.4601 −9.4553
19.6156 19.6598 34.6623 34.7157 34.6138 34.7032 34.6562
U5 2007 09 03.61656 −1.9700 U5 2007 09 03.61739 −1.8822 All satellites
0.1 −41.2 0.1 0.1 32.2 −18.0 131.2 −100.7 42.3 −40.5 28.2 −46.9 32.5 −31.2
0.5 −42.0 −3.2223 11.8538 −22.9 0.5 −0.7 −3.2139 11.8886 −17.2 20.9 −33.7 3.3295 −11.4970 38.9 120.0 −116.4 3.3486 −11.5853 51.4 31.1 −56.2 3.1013 −11.3430 −192.7 16.9 −62.7 3.2971 −11.5847 −3.2 21.3 −46.9 3.3213 −11.5410 17.6 30 ±16 38.1 5.6 −68.9 −144.1 −254.1 −144.5 −132.6
−51 ±13 −40.5 −21.5 145.8 151.6 304.1 104.8 159.3
−88 ±37
109 ±43
−100 ±38
115 ±44
4.9013 −18.2282 4.8589 −18.2024 −1.9876 6.5140 −1.3252 5.9930 −1.9656 6.6258 −1.9947 6.5332 −1.9779 6.5140
49.1 −18.4 6.1337 −13.5 −26.1 6.0644 21.3 −63.7 8.1558 67.7 −97.0 7.9544 39.2 −83.9 8.0868 41.0 −24.5 8.1204 19.1 −44.0 8.1596 32 −51 ±10 ±12 31.9 −72.5 −5.8272 37.6 −41.2 −5.8159 26.7 −48.3 −9.4978 45.3 1.6 −9.7305 94.9 −103.9 −9.4698 86.6 −17.7 −9.4228 92.2 −68.4 −9.5030 59 −50 ±12 ±13
178.1 −119.6 94.2 −30.2 0 0 ±18 ±15
in RA and Dec. referred to as 2MASS and USNO-B1.0. Moderate values of the differences between similar (O−C) in the case of sat − cm positions also adhere to the supposition about the common shift of positions of the reference stars between catalogues. On a whole, the values of (O−C) and their standard errors obtained in this work are at the same levels that are usually seen in the cases of similar observations with more wide fields of view processed using the UCAC2 as a reference catalogue (Izmailov et al. 2006). Thus, the 2MASS and USNO-B1.0 catalogues may provide sufficient accuracy of determination of the Uranian satellites’ positions in the case of a relatively small field of view of the long focal length telescope. C
(arcsec)
−40 ±12 −41.3 −22.3 137.8 143.6 296.1 96.8 151.3
8.2756 −123.0 8.1918 −33.7 0 ±15
(O−C) y x y (mas) GUST86 GUST06
x
GUST06
38 ±17 48.4 16.0 −56.6 −131.8 −241.8 −132.2 −120.3
38.1 −14.2 −24.5 −21.9 −2.9 −69.2 43.5 −102.5 15.0 −89.4 16.8 −30.0 −5.1 −49.4 12 −54 ±9 ±13 36.4 −81.5 42.1 −50.2 27.3 −50.6 46.0 −0.6 95.5 −106.1 87.3 −19.9 92.9 −70.6 61 −54 ±11 ±14
Y
y
(mas) GUST86
U1 U1 U1 U1 U1 U1 U1
X
C 2009 RAS, MNRAS 393, 1353–1358 2009 The Author. Journal compilation
173.4 −1.9855 89.5 −1.8936 0 ±18
−51.0 −22.5 −9.1 −16.8 4.7 27.6 −57.7 40.1 171.8 −203.9 −44.9 −14.4 12.5 6.4
−51.8 −9.9 −11.0 −73.4 156.0 −60.7 −3.2
−18 4 −26 −8 ±31 ±30 ±31 ±29 83.6 −25.1 73.3 −24.3 43.4 −7.5 33.1 −6.7 −90.2 112.6 −102.5 120.6 576.1 −423.1 563.8 −415.1 −60.5 195.1 −72.8 203.1 −86.0 88.8 −98.3 96.8 −65.1 54.0 −77.4 62.0 57 ±90
−1 ±76
46 ±90
5 ±76
−21.4922 80.7 4.0 91.8 −0.2 −21.5154 7.4 −5.1 18.5 −9.3 −29.6360 3.8 −23.4 28.0 −18.0 −29.4660 −198.9 151.8 −174.7 157.2 −29.6472 −67.8 −24.4 −43.6 −18.9 −29.6427 −35.4 −15.0 −11.2 −9.5 −29.6330 2.4 0.3 26.6 5.8 −30 13 −9 15 ±33 ±24 ±32 ±24 19.5988 −2.9 −98.3 −7.4 −89.3 19.6436 11.4 −66.4 6.9 −57.4 34.6190 47.5 −93.9 46.8 −91.6 34.8160 −184.5 99.6 −185.2 101.9 34.6067 76.9 −113.1 76.2 −110.9 34.6942 124.6 −28.9 123.9 −26.7 34.6600 45.1 −66.9 44.4 −64.6 17 −53 15 −48 ±37 ±27 ±37 ±27 8.2678 −138.5 8.1856 −45.1 0 ±25
170.3 −135.1 88.0 −41.6 0 0 ±21 ±25
165.6 83.3 0 ±21
AC K N OW L E D G M E N T S The author thanks Faulkes Telescopes Team and British Council, and pays special thanks to S. D. Ivanov, I. I. Sokolova, I. Yu. Aleksashina and the administration of the 353 school of the SaintPetersburg. This work was partially supported by RFBR (project 07-02-00235-a). REFERENCES Cutri R. M. et al., 2003, The IRSA 2MASS All-Sky Point Source Catalog. NASA/IPAC Infrared Science Archive (http://irsa.ipac. caltech.edu/applications/Gator)
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Table 4. Equatorial coordinates of Uranus deduced from the satellites’ positions determined with respect to USNO-B1.0 and 2MASS catalogues. Appropriate (O−C) values calculated with the DE405 and INPOP theories are presented. The values RA and Dec. are internal standard errors of Uranus positions. The mean values of (O−C) and their standard errors are displayed in separate lines. Date (UTC)
RA (h m
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
Dec. s)
23 12 50.71549 23 12 50.72665 23 12 42.00230 23 12 41.97537 23 12 41.98276 23 12 41.96063 23 12 41.96547
(◦
RA
Dec.
)
−05 56 34.8526 −05 56 34.8944 −05 57 30.2022 −05 57 30.1241 −05 57 30.2036 −05 57 30.2664 −05 57 30.4051
USNO-B1.0/GUST86 32 46 14 25 20 47 44 52 84 99 47 33 45 51 41
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 50.71580 23 12 50.72696 23 12 42.00221 23 12 41.97528 23 12 41.98267 23 12 41.96054 23 12 41.96538
(O−C) DE405 (mas)
−05 56 34.8479 −05 56 34.8897 −05 57 30.1949 −05 57 30.1169 −05 57 30.1963 −05 57 30.2591 −05 57 30.3978
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 50.73593 23 12 50.74061 23 12 42.00505 23 12 42.00632 23 12 41.99071 23 12 41.98913 23 12 41.97337
−05 56 35.0358 −05 56 34.9892 −05 57 30.4319 −05 57 30.6254 −05 57 30.4626 −05 57 30.3514 −05 57 30.5788
2007 09 03.61656 2007 09 03.61739 2007 09 04.60648 2007 09 04.60716 2007 09 04.60783 2007 09 04.60847 2007 09 04.60919
23 12 50.73624 23 12 50.74092 23 12 42.00496 23 12 42.00623 23 12 41.99062 23 12 41.98904 23 12 41.97328
−05 56 35.0311 −05 56 34.9845 −05 57 30.4247 −05 57 30.6181 −05 57 30.4553 −05 57 30.3441 −05 57 30.5716
50
USNO-B1.0/GUST06 31 44 11 23 23 49 49 54 86 102 50 36 47 53
INPOP
−384.7 −106.4 6.7 −306.1 −105.4 −351.6 −182.5
134.5 138.8 121.2 237.2 195.0 167.9 69.3
−290.8 −12.5 100.5 −212.3 −11.6 −257.7 −88.6
256.6 261.0 243.4 359.4 317.2 290.0 191.4
−204 ±56
152 ±20
−110 ±56
274 ±20
−380.0 −101.7 5.3 −307.4 −106.8 −352.9 −183.8 −203 ±56
139.2 143.5 128.5 244.4 202.3 175.2 76.6 159 ±20
−286.2 −7.9 99.2 −213.6 −12.9 −259.1 −90.0 −110 ±56
261.3 265.7 250.7 366.6 324.5 297.3 198.7 281 ±20
43
52
2MASS/GUST86 41 15 32 192 37 45 23 55
46 25 43 142 68 30 26 54
−78.1 103.0 47.9 158.2 13.8 75.9 −64.0 37 ±36
−48.7 44.0 −108.5 −264.1 −64.0 82.9 −104.4 −66 ±43
15.8 196.9 141.8 252.0 107.7 169.8 29.9 131 ±33
73.4 166.2 13.7 −141.9 58.2 205.0 17.7 56 ±43
2MASS/GUST06 40 13 34 188 35 46 27
44 23 44 139 70 34 26
−73.4 107.7 46.6 156.8 12.5 74.6 −65.3
55
54
37 ±33
−44.0 48.7 −101.3 −256.8 −56.7 90.2 −97.2 −60 ±43
20.4 201.5 140.4 250.6 106.3 168.4 28.5 131 ±33
78.1 170.9 20.9 −134.6 65.5 212.3 24.9 63 ±43
Monet D. G. et al., 2003, AJ, 125, 984 Standish E. M., 1998, JPL Planetary and Lunar Ephemerides. DE405/LE405, JPL IOM 312.F-98-048 Zacharias N., Urban S. E., Zacharias M. I., Wycoff G. L., Hall D. M., Monet D. G., Rafferty T. J., 2004, AJ, 127, 3043
Emelyanov N. V., Arlot J.-E., Varfolomeev M. I., Vashkov’yak S. N., Kanter A. A., Kudryavtsev S. M., Nasonova L. P., Ural’Skaya V. S., 2006, Cosm. Res., 44, 128 Fienga A., Manche H., Laskar J., Gastineau M., 2008, A&A, 477, 315 Hidas M. G., Christou A. A., Brown T. M., 2007, MNRAS, 384, L38 Izmailov I. S., Korotkii S. A., Ereshko M. V., Stepura A. V., 2007, Sol. Syst. Res., 41, 42 Laskar J., Jacobson R. A., 1987, A&A, 188, 212
This paper has been typeset from a TEX/LATEX file prepared by the author.
C
C 2009 RAS, MNRAS 393, 1353–1358 2009 The Author. Journal compilation
