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 measurements 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 satellites. 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 systems for many of the planets and satellites of the solar system (TAU Trwwaotbne, 1979) . The coordinate systems of synchronous satellites, 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 positions 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 ryrtem 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 poritive. 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 counting 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 satellites (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. Knowing the locations of the satellites, the wide-angle camera orien- -1 tation matrix could be detenined, and since the rtrix CNACtrA was known from the star calibrations, the narrow-angle canera orientation -1 matrix could be calculated: = Thus, in the control net computations, the camera orientation matrices of a few frames are constrained by weights. Those frames with C matrices computed from simultaneous exposures are given in Table 3. Table 3

NARRW-ANGLE PBAneS WITH ORIENTATION MATRICES OONSTRAINED BY SIMULTANEOUSLY EXPOSED WIDE-ANGLE F'RAMES

-- - -- FDS Picture 2-Pisel Surface Satellite Frame Number Rerolution (km)

Europa 16323.14 16323.18 16357.07 16357.11

Callisto 16321.59 16322.03 16323.00 16323.04 16323.08

Peale (1977) proved that, within a few degrees, the rotation axes of the Galilean satellites are normal to their orbital planes at all times. With this information, the directions of the north poles of the Galilean satellites were derived by Lieske (1979) and adopted by the IAU (Trcmsactinna, 1979). Using control net data, analytical triangula- tions were carried out in which the direction of the spin axis was treated as an unknown. The results of these computations, given in Table 4, confirm Peale's analysis and suggest that these results do not offer improvements over the 1AU recommendations. Preliminary attempts have been made to solve for a, b, and c, the principal radii of the triaxial ellipsoid which describes 10's surface. If the satellite were homogeneous and in hydrostatic equilibrium, then a - c = 15.6 km and b - c = 3.9 km (Dermott, 1979). Early results indicate that 10 is not in hydrostatic equilibrium. Computations using Table 4

tbaaured North Pole Direction IAU North Pols Direction with Emtimtad Error 6 I Satellite a. o a. 0

10 268t01 64t54 267t91 f OtOl 64356 2 0301 Europa 269tO7 643 34 268t91 f 0326 64t27 f Of06 G8nylud. 268345 64362 268356 2 Ot32 64364 f 0307 Callir to 268325 64: 62 268310 2 0t21 64t38 2 0309

5368 luuure-ntr of 319 point. on 193 picturer indicate that a - a ir leer than 4 km and b ia approximately equal to a. The erron urocirted with the rolutiona for a - a and b - a are rather large, pettrap. 5 km, ro there ia rtill conriderable uncertainty in the ruultr. If, howwar, there mauurewntr rhould be accurate, they will have importat wlica- tionr regarding the evolution, internal cowporitian, and physical state of lo. In the future, with additional work, it rhould be porrible to improve there mearurementr and lower the correrponding errorr. The ryrtem of longituder on krr (Daviu and Arthur, 1973) and Mercury (Davier and Batron, 1975) ham been defined by rurface featurer. The intent is to do the omfor the Galilean utelliter. However, at 10 it ir not obvioua how to relect a .dl, pemmmt feature which cur be identified on future mirrionr becaure of the high rate of rerurfacing due to volcanirm (Johnoon et 81.. 1979; Mrriron et a1 - 1979). For thir rearon, no change ir ruggerted for the definition of longituder on 10 from that of the IAU (Ttumrruath, 1979). Snvll craterr, am yet unnamed, near the equator8 have been relected to define the longitude ryrteaar on Europa, Cmymedc, and Chllirto.

On Europa, point 52 definer 182' longitude On Canymade, point 1000 definer 134' longitude On Callisto, point 400 def iner 326' longitude There longituder differ from tha IAU l0ngitub.r by lesr than 0%. according to tho current control net caaputrtiono. me pointr cm br raen oa TEua. 1 to 3. The Voyrer coordinate rprtem now in we for the CrlUea utelliter hrr the followin8 vrlwr for the diraction of the rpin .xir md prlw meridla in rt4nbutd Earth equator (1350.0) coorditutot -10-

Fig. 1--Point number 52 defines the 182° meridian on Europa

ORIGINAL PAGE " I OF P" QUALM Pi_N ► -11-

-1d n

t 9•

L t.

t tii ^

Fig. 2--Point number JOOC defines the 134° meridian on Ganymede

ill, pliGr r --12-

Fig. 3--Point number 400 defines the 326° meridian on Callisto -13-

-I I I. COORDINATES OF TtlE CONTROL POINTS--

The control points are selected n;~didentified on individual frames ,and their position meact~redby counting pixels on the pictures. These measurements are corrected for geometric distortions using the reseau and scaled to millimeter coordinates in the camera focal p'~ane. Thev may then be incorporated into the analytical triangulation. Control points that are easily seen are identified on U.S. Ceo- logical Survey 1:25,000,000 scale maps of the satellites, as shown in Figs. 4 through 7. Most of the points are too small to he seen on these maps, and there are too many to idectify here. A few of the points correspond to features that have been given names by the IAU Working Group on Solar System Nomenclature (Yt*tvinl.qt~ctic?rzs, 1979). To aid in their identification. they have been listed in Tables 5 tl~rough 8. The coordinates of the control points are given in Tables 9 throtigh 12. -14-

1 y

jo HO w O a

- w ^ J dT

00 O

a G O .b

W w ,-I u C N M

m iJ G O 0.

oG U

b uCJ U d r^ V

I 1

00 wrl

^I, PACHf, I -15-

a O w V w w G a b

u .a 00 O O v u

a L L C 2 N O Tom• ^^ .d v w +i u .'C bv m L r^ G O a

O w u C O U 't7 v L U v v Ln i ^n

00 w -16-

j'-40o,oA 4 lqvw^ i ♦ ^Y

-tv. P' ' pop M

w _ ^ n 0 a

t a^

00 1 ^^ O .-4

Oyy Is

G 0 r^ b v w u G i d

w m u G aO w 0 I K H L G O U ^ s .Q N V L U 61

I I ^D

00 .-i [s.

PA r; f i5 I -11-

1 i

V =o -F -- '40 O

t0 U

O gi Y ` ^ ^^^ 4 ' e o J'. C6 E I1 S R ^^9 ^tJ v ,d w f 7

cti U .100 O O

A z ark •i.^ - 3^ 1

,,^a•^; ! . ;ice .- , _ , _ Z ^^ ada v U4 ,a jo L

L C aO

O $. u C O U .b 4J L U GJ W -do f w r ' •

^ w^^ ^O Table 5

10: CONTROL POINTS IDENTIFIED BY NAMES

Con t rol Cont to1 Point Point Name Number Namc Number

Encptive Centem Patem (con t inued) Loki 29 Cib 11 25 Heno 35 h Hephaes tue 30 Silpium 62 Horus 38 Kane 163 Tho zus Loki 31 Inachus 154 Maaeaw 180 Manua 4 5 Patera Mihr 24 Amaterasu 3 3 Mueku 188 Asha 10 Atar 11 Ra 37 Babbar 1 Re idm 9 Bochia 151 Sengen 34 Daedal us U6 Svarog 86 Dazhbog 32 Ulgen 85 Emakong 4 4 Uta 137 Fuchi 46 Galai 17

Table 6

EmpA: C0-L POINTS IDENTIFIED BY Nm

Name Control Point Number

Macu Za Thera 33 5 re 15 Table 7

GANYMEDE: CONTROL POINTS IDENTIFIED BY NAMES

Name Control Point Nuder mters Achelous Aeshur AY~ Dane1 Enlil Eahmun Etana Khumb am Kiahar Melkart Namtar Nut Sapas Sebek Sin 116 Table 8

CALLISTO: CONTROL POINTS IDENTIFIED BY NAMES

Control Control Point Point Number Number

Lurge-Ringed Feat- Cmtens (continued) Ae gard Wdr Valhalla Habrok Haki Crdens Har Ada1 Hepti Agroi Hodr Aky cha Hogni All Igala Anarr Jumo Aningan Karl Askr Balkr Karl Bavorr Losy Beli Me ra Mimir Brag1 Modi Brad Nama Buga Nar Burl Burr Nerivik Danr Nidi Dia Nor1 Dr'Yops Durinn Oski Egdir Otta Pekko Erlik Sarakka Fadir Seqinek Fill Sholmo Finnr Sigyn Freki Skoll Frodi Sudr i Fulla Sumbur Fulnir Geri Tindr GIsi Valfodr Vali Gloi Vestri Go 11 Vitr Gondul Ymir Grimr Gunn r Tabla 9

Point ht. Long. Point ht. w. Point kt, Long, Table 9-!bnt inued

Point Point Lat. Long. Point Long.

348.0 9.4 34.4 uo, 5 23.3 328.9 324-4 325.3 334.6 340. 8 Table 9--Continued)

Point Lat . Long. Point Lat. Long. Point -24-

Table 10

EmOPA: CmRDI~T'Eso? OanT#)t POXIIPS (degraea)

Paint kt. Long. Poiat kt. Loag. Point kt. Long. rt. t -26.3 10.5 -16.2 23. 8 -9.7 1700 45. s -4.7 18.0

Jto 9 -29.0 9.3 42.9 28.3 -55. 6 -47m 3 -18 1 -69.5 -13.7

-20.4 -10.5 -9.0 -29.6 3. 8 16 6 28.6 3.8 -47.7 -12mS

-5.4 -42.2 -36.9 -37.4 -4.7 -5.9 mt:COORDIlA' OP POINTS

Point kt. -8. Point ht. -8, Point Itrt. Lana.

325.0 314o7 31 1. 1 341.1 16.5 90 8 so. 2 400 9 309.9 357m9 -26-

GANYMEDE Table 11--Continued

Point Lat . Long. Lat. Long. Point Long.

165 0.7 339.4 70. 2 3540 Y 261 24. 1 166 -18.9 1405 32.5 237.4 262 21. 0 167 -20.8 12. S 37.7 197.7 265 358. 3 168 -10.1 11.9 34.7 150.9 266 339e2 169 -9. U 6.0 -4.2 185.9 267 64.8 170 -16.8 7.5 -4.9 q79.1 268 55.7 171 -17.3 2. 1 6.5 1630 3 269 SO. 6 175 -13.1 336.4 2e8 162.6 270 356-3 177 -20.5 328.9 -6.5 193.1 271 6.1 178 20. 1 1309 11.6 189. 7 2 72 326.9 179 18.3 20.9 3.0 191.5 273 23. 1 180 14.3 15.5 23.8 177.3 274 322. U 18 1 9.1 10.3 23.0 170.3 275 330.9 182 13.9 24.9 32 0 171.8 276 324.2 183 30.2 27.5 9.4 21 507 2 77 29- 5 1 84 32.9 341.2 10.3 229.4 278 220 5 185 28.5 3U4.6 4. 6 202.4 279 17.5 188 40.3 320. 1 -11.0 168.5 280 33.6 190 36.6 314.9 -6.3 149.1 28 1 135.4 19 1 -40.6 339.1 -18.6 185.0 282 156.0 GANYMEDE TaL le 11--Continued

Point Let. Long. Point Lat. Long. Point Lat . Long.

500 502 503 504 5011 SOY 510 512 515 519 G-DE Table 11--Continued

Point Lat. Long. Point Lat. Long. Point Lat. Table 11--Cont inued

Point Lat. Long. Point Lat. Long. Point Lat. Long. GANYMEDE Table 11--Continued

Point Lal. Long. Point Lat. Long. Point Lat . Long. Table 11- 4ont inued

Point Lat. Long. Point Lat. Long. Point Lat. Long.

173;j 131.5 ?6o.d 154.6 142. L 10J.o 143. b 21. 5 Is. 7 Lb. 1 CANYMEDE Table 11--Continued

Point Lat. Long. Point Lat . Long. Point Lat . Long. Table 12

CALLISTO: COORDINATES OF CONTROL POINTS

(degreer)

Point Lat . Long. Point Lat. Long. Point Lat. Long. Table 12--Cont inued

Point Lat. Long. Point Lat . Long. Lat. Long.

LJU 235 236 237 238 239 240 241 242 243

I64 2 ou 1 b5 105 Ibb 2 Oti 107 2 07 168 LOB 169 L 39 170 210 17 1 21 1 172 212 17J L13 CALLISTO : Table 12--Continued

Point Lat. Long. Point Lat. Long. Point Lat . Long.

53. 1 64.6 65.0 -21.9 us. 4 55.8 56.5 5.6 22.2 51.8 Point Lat. Point Lat. Long. Point Long, -37-

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