In a joint JPL-STL effort the planetary ephemerides have been collected on IBM 704-709 magnetic tape, and a series of routines have been written to utilize these tapes. This paper describes the contents and preparation of the ephemeris tapes

Hudson, R. H.

English

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J E T  P R O P U L S I O N  L A B O R A T O R Y  
C A L I F O R N I A  I N S T I T U T E  O F  T E C H N O L O G Y  
P A S A D E N A .  C A L I F O R N I A  
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National .4eronautics and Space Administration 
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PLANETARY EPHEMERIDES -... 
R .  H. Hudson 
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JET PROPULSION 
A Research F 
National Aeronautics a i d  S 
November 2, 1960 
JPL Technical Release No. 34-239 
CON TENTS 
I 
Subtabulated Lunar and Planetary Ephemerides . . . . . . . . . . . . . . . . . .  1 
R e f e r e n c e s . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5 
Appendix: Tape F o r m a t .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6: 
JPL Technical Release No. 34-239 . 
~ ~ _ _ _  
SUBTABULATED LUNAR AND PLANETARY EPHEMERIDES~ 
In a joint JPL-STL effort  the planetary ephemerides have been collected on 
IBM 704-709 magnetic tape, and a ser ies  of routines have been written to utilize these 
tapes. This paper describes the contents and preparation of the ephemeris tapes. 
T w o  tapes a r e  available, a geocentric tape containing the Cartesian coordinates 
of the planets, the Sun, and the Moon tabulated a t  one-day intervals for the period 
J. D. 24371 16. 5 to 24441 132. 5 and a heliocentric tape containing the Cartesian coordin- 
ates of the planets and the Earth-Moon barycenter tabulated a t  4-day intervals for  the 
period J. D. 2437116. 5 to 2451716. 5. 
mean equator and equinox of 1950. 0. 
of the Moon, which is tabulated in Earth radii. 
Appendix. 
Both coordinate systems a r e  referred to the 
All coordinates a r e  in A. U. with the exception 
The tape format  is described in the 
Due to lack of source data the  position coordinates of Mars and Mercury a r e  
replaced with zeros  on the heliocentric tape after J. D. 2450996 and J. D. 2443880. 5, 
respectively. 
Table 1 indicates the source of the ephemerides used in preparing the tapes 
and gives the tabular interval (in days) of the data. 
Moon, which were obtained in geocentric coordinates, all ephemerides w e r e  in the 
heliocentric coordinate system, referred to the mean equinox and equator of 1950. 0. 
With the exception of the Sun and 
This paper presents the results of one phase of research carried out at the 1 
JPL Technical Release No. 34-239 
Table 1 
Body 
Pluto 
Neptune 
Uranus 
Saturn 
Jupiter 
M a r s  
Earth - Moon 
Muon 
Venus  
hl e r  c u r  y 
Sun 
Interval 
40 
40 
40  
40 
40  
20 
4 
4 
1 1 2  
5 
4 
Source 
Astronomical Papers,  Vol. XI1 
It 
W 
It 
I1 
U.  S. Naval Proving Ground 
Astronomical Papers ,  Vol. XIV 
U. S. Naval Observatory 
Astronomical Papers,  Vol. XV, 
Pa r t  I11 
Plan eta ry  Coordinates 
Astronomical Papers,  Vol. XIV 
The data from the Astronomical Papers were obtained in the form of magnetic 
tape copies of the "Themis Tapes" which w e r e  prepared from the Astronomical Papers  
by the University of California Radiation Laboratory. The lunar ephemerides were 
obtained in geocentric rectangular coordinates for the period 1960-1970 in groups of 
approximately one year,  each group referred to the equinox of nearest  beginning of 
year. These data were then rotated s o  that the coordinate system was referred to the 
equinox of 1950. 0. 
Since the ephemerides w e r e  being prepared primarily for interplanetary t r a  - 
jectory computations, the tabular interval was chosen to be constant for each body to 
ease the programming required to use the tapes. Further,  i t  w a s  decided to ca r ry  
second and fourth central differences so that an Everett method could be used to speed 
the interpolation process. With this in mind, the inclusion of the Moon dictated a 
maximum interval of one day for the geocentric tape, and the inner planets dictated a 
4-day interval for the heliocentric tape. 
2 
JPL Technical Release No. 34-230 
Even though one day is an  unnecessarily fine interval for the geocentric 
coordinates of the planets, it was found necessary to c a r r y  modified second and modi- 
fied fourth differences for the Moon, in effect "throwing back" the sixth and eighth 
differences of the lunar position onto the second and fourth differences. 
of this technique can be found in References 1 and 2.  
throw -backs are 
A discussion 
The formulas for  simultaneous 
d2 = b2 - 0.01312 b6 + 0.0043 d 8 m 
d4 = b4 - 0.27827 d6 + 0.0685 h8 
m 
Representative samples of the source data w e r e  differenced to determine t h e  
optimum polynomial to u s e  in subtabulating. 
differences to find which differences could be neglected was backed up by estimating 
the "noise" in the data and computing how the noise would propagate through the differ- 
ence table. 
tion of the "noise" it was assumed that they, and higher differences, could be ignored. 
The usual method of "eye balling" the 
When the actual differences became smaller  than the estimated propaga - 
Table 2 gives the order  of the polynomial used to subtabulate each body. The 
differences were such that the same  interpolating polynomial could be used for each 
position component of any given planet. 
JPL Technical Release No. 34-239 
Body 
Pluto 
Uranus 
Saturn 
Jupiter 
Mars 
Earth -Moon 
Venus 
Mercury 
Sun 
Neptune 
Table 2 
Polynomial Order  
3 
3 
3 
4 
5 
8 
4 
5 
6 
5 
The Mercury data were available only to three significant figures and the interpolation 
order  chosen w a s  completely arbitrary.  Mercury was included solely for complete - 
ness.  
The ephemerides were subtabulated to 1 - and 4 -day intervals using polynomials 
To obtain geocentric coordinates of the planets, the geo- of the order  indicated above. 
centric coordinates of the Sun were added to the heliocentric coordinates of the planets. 
‘The signs of the solar  geocentric coordinates were changed to obtain the heliocentric 
coordinates of the Earth. 
F o r  each of the source ephemerides the f i r s t  differences assumed to be neglig- 
ible were listed for the period of interest and scanned for bad points. 
was not feasible in the lunar case  due to the magnitude of the high order  differences. 
The sixth central differences of the Moon’s position were plotted and scanned to check 
for bad points. 
This procedure 
To guard against gross errors in the subtabulation process the f i r s t  negligible 
differences for each planet on the final tapes were  again listed and scanned for bad 
points. 4 
JPL Technical Release No.  34-239 
REFERENCES 
1. H. ILI. Nautical Almanac Office, Interpolation and Allied Tables, H. &I. Station- 
e ry  Office, London, 1956. 
2 .  Kopal, Zdenek, Numerical Analysis, John Wiley and Sons, New York, 1955. 
3 .  Nautical Almanac Office, U. S. Naval Observatory, Astronomical Papers ,  Vol.  
X I ,  XIV, XV. U .  S. Government Printing Office, Washington, 1951 , 1953, 1955. ' 4. H. M. Nautical Almanac Office, Planetary Co-ordinates 1960-1980, H. M. Sta- 
tionery Office, London, 1958. 
I 
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5 
i 
R 
I 
I 
I 
1 
II 
I 
I 
I 
JPL Technical Release No. 34-239 
APPENDIX 
TAPE FORMAT 
The formats of the geocentric tape and the heliocentric tape are identical. All 
data a r e  written in the low density binary mode. The tape begins with one record 
describing the contents of the tape followed by one record per  Julian day tabulated. 
An end-of-file mark follows the las t  record. 
ber 000000000001, and this number is not included in the checksum which follows each 
Each record begins with the octal num- 
record.  This is a dummy word included for compatibility with FORTRAN programs. 
A.  I .  D. Record (length 2N+6) 
PZ E 1 
PZE 0, 0, xxx 
PZ E 0, 0, N 
BCI 2, Sun 
BCI 2, Mercury 
BCI 2, Venus 
BCI 2, Earth-Moon 
Check-sum 
B. General record (length 9N+3) 
PZE 1 
DEC J u l i a  Date 
DEC x, Y, z 
DE C 62X, 62Y, 6 2 2  
DEC 64X, 64Y, 6 4 2  
DEC X, Y, Z, etc. 
Check-sum 
(For  FORTRAN compatibility ) 
Table number 
Number of bodies tabulated 
Name of central body 
BCD names of tabulated bodies 
( 2  words per name) 
Does not include f i r s t  word 
Dummy word 
1st tabulated body 
2nd tabulated body 
Does not include first word 
6 


Subtabulated Lunar and Planetary Ephemerides

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