KPL/PCK
From: Bill L. Taber
Date: Wed, 27 Apr 94 12:12:59 -0700
To: wright@miranda.ssec.wisc.edu
Subject: Re: J2 values for Sol Sys bodies
Cc: btaber
From: Bill L. Taber
Date: Mon, 25 Apr 94 15:56:03 -0700
To:
Subject: Re: J2 values for Sol Sys bodies
Cc: btaber
Hi Ed.
I need to supply a few corrections to the data I sent you concerning
gravity models for solar system bodies. I have a "better" estimate
for J2 of Mercury and it turns out the data I gave you for Venus
is "normalized" So below are the improved values. I've sent everything
again just for your convenience. Also you can simply use this
mail message as an input to LDPOOL.
Oh yeah, we do have ephemerides for Galileo and Clementine somewhere.
I need to do a bit of digging to locate them.
\begindata
BODY399_J2 = 1.082616D-3
BODY399_J3 = -2.53881D-6
BODY399_J4 = -1.65597D-6
BODY4_J2 = 1.964D-3
BODY4_J3 = 3.6D-5
BODY499_J2 = 1.964D-3
BODY499_J3 = 3.6D-5
BODY599_J2 = 1.475D-2
BODY599_J4 = -5.8D-4
BODY699_J2 = 1.645D-2
BODY699_J4 = -1.0D-3
BODY799_J2 = 1.2D-2
BODY899_J2 = 4.0D-3
\begintext
Nicole Rappaport in the gravitational dynamics group here has
been working on the gravity field for Venus and gave me the
following values. I've adjusted them to remove normalization
factors.
\begindata
BODY2_J2 = 4.441139399E-06
BODY2_J3 = -2.071395599E-06
BODY2_J4 = -2.160986924E-06
BODY299_J2 = 4.441139399E-06
BODY299_J3 = -2.071395599E-06
BODY299_J4 = -2.160986924E-06
\begintext
The best value I have for Mercury is:
\begindata
BODY1_J2 = 6.0D-5
BODY199_J2 = 6.0D-5
\begintext
However this estimate is given in the source as (6+-2)D-5 so you
can take that for what it's worth.
For the moon:
begindata
BODY301_J2 = 2.024D-4
\begintext
GM values of bodies
--------------------------------------------------------
The GM values given below are stated with high precision to avoid
loss of significance due to finite precision arithmetic; the actual
number of significant digits in these values is generally much lower
than the number of digits shown. For planetary systems, the ratio of
the Sun's GM to the system's GM is stated using only significant digits;
the same is true for the ratios of satellite GMs to the GMs of the
corresponding planets.
The Astronomical Unit
The value of k and the relation between k and the GM of the
Sun are from the ``Explanatory Supplement to the
Astronomical Almanac,'' 1992. P. 696.
The astronomical unit AU is given in kilometers.
\begindata
AU = ( 149597870.7 )
\begintext
The GM of the Sun was derived from the formula
3 2 2
GM = AU k / D
Sun
where k is the Gaussian gravitational constant
0.01720209895
D is 86400 ephemeris seconds, and AU is given in units of
kilometers.
The Sun
\begindata
BODY10_GM = ( 132712440041.94 )
\begintext
Mercury
Sun GM / Mercury system GM = 6023600.
BODY1_GM/PRIMARY = ( 0.16601367952719300D-06 )
\begindata
BODY1_GM = ( 22032.08049039435 )
BODY199_GM = ( 22032.08049039435 )
\begintext
Venus
Sun GM / Venus system GM = 408523.7
BODY2_GM/PRIMARY = ( 0.24478383995836710D-05 )
\begindata
BODY2_GM = ( 324858.6068371049 )
BODY299_GM = ( 324858.6068371049 )
\begintext
The Earth-Moon System
Sun GM / Earth system GM = 328900.56
BODY3_GM/PRIMARY = ( 0.30404326462685300D-05 )
BODY301_GM/PRIMARY = ( 12150580.D-9 )
\begindata
BODY3_GM = ( 403503.2352694668 )
BODY301_GM = ( 4843.941639988467 )
BODY399_GM = ( 398659.29362947830 )
\begintext
The Martian System
Sun GM / Mars system GM = 3098708.
BODY4_GM/PRIMARY = ( 0.32271514450538740D-06 )
BODY401_GM/PRIMARY = ( 19.9D-9 )
BODY402_GM/PRIMARY = ( 28.0D-10 )
The GM of Phobos given in Jacobson's report is slightly off;
the correct value has been computed from the GM/primary
ratio and the GM of Mars.
\begindata
BODY4_GM = ( 42828.31426579703 )
BODY401_GM = ( 85.22834344572990D-5 )
BODY402_GM = ( 119.9192772100721D-6 )
BODY499_GM = ( 42828.313289311500 )
\begintext
The Jovian System
Sun GM / Jupiter system GM = 1047.3486
BODY5_GM/PRIMARY = ( 0.95479193842432210D-03 )
BODY501_GM/PRIMARY = ( 4705.3D-8 )
BODY502_GM/PRIMARY = ( 2526.7D-8 )
BODY503_GM/PRIMARY = ( 7804.3D-8 )
BODY504_GM/PRIMARY = ( 5668.3D-8 )
BODY505_GM/PRIMARY = ( 4.D-9 )
BODY506_GM/PRIMARY = ( 4.D-9 )
BODY507_GM/PRIMARY = ( 3.D-10 )
BODY508_GM/PRIMARY = ( 9.D-11 )
BODY509_GM/PRIMARY = ( 3.D-11 )
BODY510_GM/PRIMARY = ( 3.D-11 )
BODY511_GM/PRIMARY = ( 5.D-11 )
BODY512_GM/PRIMARY = ( 2.D-11 )
BODY513_GM/PRIMARY = ( 2.D-12 )
BODY514_GM/PRIMARY = ( 8.D-10 )
BODY515_GM/PRIMARY = ( 7.D-12 )
BODY516_GM/PRIMARY = ( 5.D-11 )
\begindata
BODY5_GM = ( 126712767.8806649 )
BODY501_GM = ( 5960.981613781674 )
BODY502_GM = ( 3200.988724107317 )
BODY503_GM = ( 9886.997387719448 )
BODY504_GM = ( 7180.972962701350 )
BODY505_GM = ( 5.067461470071345D-1 )
BODY506_GM = ( 5.067461470071345D-1 )
BODY507_GM = ( 3.800596102553509D-2 )
BODY508_GM = ( 11.40178830766053D-3 )
BODY509_GM = ( 3.800596102553508D-3 )
BODY510_GM = ( 3.800596102553508D-3 )
BODY511_GM = ( 6.334326837589181D-3 )
BODY512_GM = ( 2.533730735035672D-3 )
BODY513_GM = ( 2.533730735035672D-4 )
BODY514_GM = ( 10.13492294014269D-2 )
BODY515_GM = ( 8.868057572624853D-4 )
BODY516_GM = ( 6.334326837589181D-3 )
BODY599_GM = ( 126686536.75178400 )
\begintext
The Saturnian System
Sun GM / Saturn system GM = 3497.90
BODY6_GM/PRIMARY = ( 0.28588581720460840D-03 )
BODY601_GM/PRIMARY = ( 65.0D-9 )
BODY602_GM/PRIMARY = ( 21.0D-8 )
BODY603_GM/PRIMARY = ( 108.5D-8 )
BODY604_GM/PRIMARY = ( 190.0D-8 )
BODY605_GM/PRIMARY = ( 40.6D-7 )
BODY606_GM/PRIMARY = ( 23669.6D-8 )
BODY607_GM/PRIMARY = ( 5.D-8 )
BODY608_GM/PRIMARY = ( 27.9D-7 )
BODY609_GM/PRIMARY = ( 24.D-9 )
BODY610_GM/PRIMARY = ( 35.6D-10 )
BODY611_GM/PRIMARY = ( 98.9D-11 )
BODY612_GM/PRIMARY = ( 3.D-11 )
BODY613_GM/PRIMARY = ( 10.D-12 )
BODY614_GM/PRIMARY = ( 7.D-12 )
BODY615_GM/PRIMARY = ( 3.D-11 )
BODY616_GM/PRIMARY = ( 9.D-10 )
BODY617_GM/PRIMARY = ( 6.D-10 )
BODY618_GM/PRIMARY = ( 7.5D-12 )
\begindata
BODY6_GM = ( 37940604.37460744 )
BODY601_GM = ( 2.465530579037799 )
BODY602_GM = ( 7.965560332275966 )
BODY603_GM = ( 41.15539505009249 )
BODY604_GM = ( 72.06935538725874 )
BODY605_GM = ( 154.0008330906687 )
BODY606_GM = ( 8978.172706706628 )
BODY607_GM = ( 1.896561983875230 )
BODY608_GM = ( 105.8281587002378 )
BODY609_GM = ( 9.103497522601104D-1 )
BODY610_GM = ( 13.50352132519164D-2 )
BODY611_GM = ( 37.51399604105205D-3 )
BODY612_GM = ( 11.37937190325138D-4 )
BODY613_GM = ( 3.793123967750460D-4 )
BODY614_GM = ( 2.655186777425322D-4 )
BODY615_GM = ( 11.37937190325138D-4 )
BODY616_GM = ( 3.413811570975414D-2 )
BODY617_GM = ( 22.75874380650276D-3 )
BODY618_GM = ( 28.44842975812845D-5 )
BODY699_GM = ( 37931239.677504600 )
\begintext
The Uranian System
Sun GM / Uranus system GM = 22902.98
BODY7_GM/PRIMARY = ( 0.43662440433515630D-04 )
BODY701_GM/PRIMARY = ( 15.6D-6 )
BODY702_GM/PRIMARY = ( 13.5D-6 )
BODY703_GM/PRIMARY = ( 40.6D-6 )
BODY704_GM/PRIMARY = ( 34.7D-6 )
BODY705_GM/PRIMARY = ( 75.9D-8 )
BODY706_GM/PRIMARY = ( 2.D-10 )
BODY707_GM/PRIMARY = ( 3.D-10 )
BODY708_GM/PRIMARY = ( 8.D-10 )
BODY709_GM/PRIMARY = ( 3.D-9 )
BODY710_GM/PRIMARY = ( 2.D-9 )
BODY711_GM/PRIMARY = ( 5.D-9 )
BODY712_GM/PRIMARY = ( 12.D-9 )
BODY713_GM/PRIMARY = ( 18.D-10 )
BODY714_GM/PRIMARY = ( 3.D-9 )
BODY715_GM/PRIMARY = ( 6.D-8 )
\begindata
BODY7_GM = ( 5794549.008117694 )
BODY701_GM = ( 90.38545171996032 )
BODY702_GM = ( 78.21817937304257 )
BODY703_GM = ( 235.2339320404095 )
BODY704_GM = ( 201.0496906847835 )
BODY705_GM = ( 4.397599862528838 )
BODY706_GM = ( 11.58787842563594D-4 )
BODY707_GM = ( 17.38181763845391D-4 )
BODY708_GM = ( 4.635151370254375D-3 )
BODY709_GM = ( 17.38181763845391D-3 )
BODY710_GM = ( 11.58787842563594D-3 )
BODY711_GM = ( 2.896969606408984D-2 )
BODY712_GM = ( 6.952727055381562D-2 )
BODY713_GM = ( 10.42909058307234D-3 )
BODY714_GM = ( 17.38181763845391D-3 )
BODY715_GM = ( 3.476363527690781D-1 )
BODY799_GM = ( 5793939.2128179700 )
\begintext
The Neptunian System
Sun GM / Neptune system GM = 19412.24
BODY8_GM/PRIMARY = ( 0.51513890205355000D-04 )
BODY801_GM/PRIMARY = ( 2089.1D-7 )
BODY802_GM/PRIMARY = ( 3.D-7 )
BODY803_GM/PRIMARY = ( 15.D-10 )
BODY804_GM/PRIMARY = ( 4.D-9 )
BODY805_GM/PRIMARY = ( 2.D-8 )
BODY806_GM/PRIMARY = ( 3.D-8 )
BODY807_GM/PRIMARY = ( 6.D-8 )
BODY808_GM/PRIMARY = ( 6.D-7 )
\begindata
BODY8_GM = ( 6836534.065205220 )
BODY801_GM = ( 1427.920574621435 )
BODY802_GM = ( 2.050529761076207 )
BODY803_GM = ( 10.2526488053810D-3 )
BODY804_GM = ( 2.734039681434943D-2 )
BODY805_GM = ( 13.67019840717471D-2 )
BODY806_GM = ( 20.50529761076207D-2 )
BODY807_GM = ( 4.101059522152414D-1 )
BODY808_GM = ( 4.101059522152414 )
BODY899_GM = ( 6835099.2035873600 )
\begintext
The Plutonian System
Sun GM / Pluto system GM = 140000000.
BODY9_GM/PRIMARY = ( 0.71428571428571430D-08 )
BODY901_GM/PRIMARY = ( 8.4D-2 )
\begindata
BODY9_GM = ( 947.9460002995671 )
BODY901_GM = ( 73.45707013391480 )
BODY999_GM = ( 874.48893016565220 )
\begintext
That's about it for now. If you have any questions or need more specific
information let me know.
Best Regards
Bill