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Coordinates of Features on the Galilean Satellites

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Coordinates of Features on the Galilean Satellites N O T I C E THIS DOCUMENT HAS BEEN REPRODUCED FROM MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE (ti AS A-CR- 163582) COOBDINATES OF FEATUBBS OY THE GALILEAil SATELLITES (BANE COXPI) 39 P nc ao3/a~ AOI CSCL 938 COORDINATES OF FEATURES ON THE GALILEAN SATELLITES Merton E. Davies and Frank Y. Katayama June 1980 The authors would like to express their thanks to Brad SPith and all of their colleagues on the Imaging Science Team for their help and Interest in acquiring the data for this experiment and for their stimulating discwsions during the mission planning phases and the exciting Jupiter encounters. We would like to thank Mary Bmell and Candice Hansen of JPL for preparing the picture-taking sequences for this experiment and Peter Kupferman, Larry Tietze, and Linda Morabido of JPL for star exposure data, star coordinates, and star plots. We are indebted to Leonard Dicken, Andrey Sergeyevsky, and Jams Campbell of the Voyager Navigation Team for trajectory updates and to Frances Popescu of JPL for putting these data in nuchinereadable form for the Rand computer, The maps used in the figures were prepared by the USGS, Flagstaff, under the direction of Raymond M. Batson. Patricia M. Bridges (So and Callisto) and Jay L. Inge (Europa and Ganymede) made the surf ace inter- pretations and beaut iful airbrush renditions. James A. Roth, Thomas A. Hauge, and David Douglas8 of Rand were responsible for the selection, identification, and measurements of the control points on the individual pictures. We are appreciative of their dedication and care in carrying out this important part of the work. This task was carried out at Rand under JPL Contract No. 953613 and NASA Contract No. NASW-3210. I. INTRODUCTION One product of the current exp1dratio.i s i the solar system is the publication of maps of those bodies with solid surfaces. These maps shw the relative positions of topographic features, one-to- another, and are used as bases for correlating a variety of measure- ments and pictorial data and for rcgional geologic mapping. In order to produce a map of a planetary surface, it is necessary to first establish a coordinate system for the body and then to deter- mine the latitudes and longitudes of topographic features in this coordinate system. It is the purpose of this paper to define the coordinate systems of each of the Galilean satellites and to present coordinates of features seen in the Voyager pictures of these satel- lites. The two Voyager encounters with Jupiter are described in -Smith et al. (1979a.b). A preliminary report on the progress of the control nets of the Galilean satellites was published by Davies et al. (1979). The method for computing the control net of these satellites is essentially the same as that used at Mars (Davies, 1972; Davies and Arthur, 1973) and at Mercury (Davies and Batson, 1975) and will not be reviewed here. Each spacecraft carried two cameras, one with a wide-angle lens and one with a narrow-angle lens. They can be shuttered independently or simultaneously. Pictures were taken of the Pleiades and other star clusters for calibration--ueing the known coordinates of the stars seen in the pictures, the camera orientation matrices, C, can be determined as well as the focal distances of the camera lenses. The focal distances of the Voyager 1 cameras are 200.293 m and 1500.19 mm, and those of the Voyager 2 cameras are 200.770 lam and 1503.49 nun (Davies et al., 1979). The matrix relating the orientation of the wide-angle canrera to that of the narrow-angle camera can be computed -1 from frames taken simultaneously by each camera. This matrix, CNAt+*, is given in Table 1 (Davies et al., 1979). Table 1 "E MATRIX c&: ~LATINGME CAMERA AIMING AND ROTATION DIRECTIONS OF THE NO WRAS ON EACH SPACECRAFT Voyager 1 0.9999950588 -0.0031011413 0.00051514M 0.0031009104 0.9999950916 0.0004483927 I-0.0005165310 -Om0O04467931 0.999999 76681 11. THE SATELLITE COORDINATE SYSTES The International Astronomical Union has defined coordinate sys- tems for many of the planets and satellites of the solar system (TAU Trwwaotbne, 1979) . The coordinate systems of synchronous satel- lites, like the Galilean satellites, are based on a resolution adopted in 1973 (IAU Tmmactwns , 1974). These IAU-reco~rsaended coordinates were the starting point for the Voyager coordinate systems of the satellites. The IAU Traneactwns, 1979, contain expressions for the direction of the north poles and the position of the prime meridians of the four satellites. These expressions are given in standard Earth equatorial coordinates of 1950.0 and, except for the rotation term in the posi- tions of the prime meridians, vary slowly with time. Because the two Voyager spacecraft encounters with Jupiter were separated by only four months, the directions of the north poles were computed at a single time and assumed constant for both encounters (Davies et al., 1919). The angle W is measured along the satellite's equator in an easterly direction with respect to the satellite's north pole from the ascend- ing nods of the satellite's equator on the standard Earth equator (1950.0) to the point where the prime meridian crosses the satellite's equator. This led to the following values: Europa oro = 269307 60 = 64334 W = 15639 + 10133747235d Ganymede a,, = 268:45 6, 1 64362 W = 19538 + 5033176081d A point, P, on the rurface of a ratellite hu cartographic coot- dituter latitude #, weat langitudo A, aid radiur R, and rectangular coordinrter X, Y, 2, where X = R cor 4 cor (360. - A), Y = R wr (O ria (360' - A), and 2 = R ain 4. Becrrure the X, Y, 2 cootdilute ryr- tem is right-handed, 360. - A ir urrd in the errpreraionr for I( 8nd Y. The Z doir the axir of rotation of the ratellite with north pori- tive. The X axis liea in the plane of the equator, poritive in the direction of 0' longitude. The Y axir liar in the plane of the eqw- tor, poritive in the direction of 270' west longitude. The rtandard equatorial coordinates of 1950.0 of the point Px, P , PZ can be Y exprersed ar where -sin(ao+900) cos(90°-do) rin(ao+900) sin(90°-60) cos (a0+9O0) cos (90'-6,) ms (a0+9O0) sin(90~-6,) 0 rin(90°- 8) co~(90~-6~) 1 and V= 1;sin Ww -1:: ;] If a picture containing P is taken by the spacecrait at Sx. Sy. Sz. the coordinater Xc, Ye of P on the picture are given by when and f ir the calibrated principal distance (focal length) and C im the trmufo~arrtionmatrix from rtandard coordinateo of 1950.0 into the camra coordinate ryrtem. Xc, Ye, f an expreosed in milli~teraand S are in kilometers. R, PX, Py, PI, Sx, S11' Coordinate, of the point P are mamured on the picture by count- ing pixel8 (picture elementr) and then reo~vingthe vidicon dirtortiom and rcaling the pixel coordi~terto mlllifmter coordinateo Xo, Yo at the faceplate of the vidicon. The rereau is wed in thlm tranrforma- tion. The pixel meauureacntr on the picturem are ertiaated to the one-tenth pixel and in general are repeatable to a few tenths of a pixel. Standard photogramactric methodm are umed to rolve for the un- knanu (ree, for evle, Davies and Arthur, 1973). Apprordarrte valuer of a11 parameterr are required to ir,itiate the analytical triangulation. The triangulation ir a problem in leut rquarer derigned to dnimite the rum of the square6 of the ruidlulm, i.e., (Xo - X,), (Yo - Ye). Observation equations are exprused in teraar of thore parameter. whore valuer are permitted to vary; the norm81 equations are formed and rolved to give improved valuer to the derired parameterr. In practice, the rpacecraft poritiono Sx, S Sz are never permitted to vary, and Y' the angler of the C matrix are wually variable, a0 are the latitude 4 and longitude X of the control poiirts. The radium at the control points can be fixed, a single man radium determined for all points, or the radium at each point determined independently. The control netr of the satelliter are computed by meanr of mingle-block analytical triangulationr. The normal equationm are rolved by the conjugate gradient iterativr mthod, which la conve- nient and converge6 rapidly a8 the initial ertiaaater of the parameterr are very good. A 8-ry of the control net computations is 8iv.n in Table 2. Table 2 StMUY OF CONTROL NET COMPUTATIONS OF THE GALILEAN SATELLITES Parameter 10 Europa Ganymede Cnllirto Points 355 106 865 375 Pictures 210 103 137 161 Obsenmtion equations 6230 20 86 6392 4358 Nowel equations 1340 521 2141 1233 Overdeterminat ion factors 4.65 4.00 2.99 3.53 Standard error of wasurement , mm 0.02148 0.01497 0.03769 0.02197 Mean radius, km 181e5 1569+_10 2631tlO 2400+10 The spacecraft trajectories used in the analytical triangulatione result from a study by the JPL Voyager Orbit Determination Group, headed by Jams K. Campbell. This study used pictures taken and re- duced by the Optical Navigation Group to update simulta~~eouslythe two Voyager trajectories and the ephemerides of the four Galilean satellites. The spacecraft positions relative to the centers of mass of the satel- lites (SxD SyD Sz) are required for the analytical triangulation8 . During the picture-taking sequences it was possible occarionally to take simultaneous pictures with the wide-angle and narrow-angle cameras in which two satellites were in the wide-angle frame and one of them with useful surface detail was in the narrow-angle frame.
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