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1988-03-01
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Comparison of planetary programs based on Jean Meeus' "Astronomical
Formulae for Calculators" (Willmann-Bell, 1986) with the JPL DE200
numerical integration.
The programs computed heliocentric geometric positions, using
Meeus' perturbations and mean element formulas for fixed equinox
J2000. Both the DE200 and Meeus positions were then precessed to
the equinox of date where their absolute difference was noted.
Beyond the errors in Meeus' expansions there is always a possibility
of mistakes in the computer program. Therefore the results should
be regarded as applying to the particular programs, applying only
perchance to the actual Formulae.
-- Steve Moshier
Legend:
Span Dates of the boundaries of the test intervals are
2378640.5 5/25/1800
2396758.5 1/1/1850
2415020.5 1/1/1900
2433282.5 1/1/1950
2451544.5 1/1/2000
2469807.5 1/1/2050
Ldate Julian date of maximum longitude error noted. Dates
of maximum latitude and radius error were not recorded.
Long Maximum error in ecliptic longitude, arc seconds.
Lat Maximum error in ecliptic latitude, arc seconds.
Radius Maximum error of radius vector, in multiples of
0.0001 astronomical unit.
Samping interval - The time in days between the points at
which positions were computed and compared.
Span Ldate Long Lat Radius
Years A.D. JD " " 10^-4 AU
--------- --------- ----- ----- -----
Mercury
sampling interval = 2.625 days
1800-1850 2387812.2 13.29 3.32 .159
1850-1900 2400391.2 12.61 3.86 .156
1900-1950 2432678.8 12.33 3.28 .141
1950-2000 2449302.9 13.97 3.93 .159
2000-2050 2461879.3 13.43 3.42 .152
Venus
sampling interval = 3.875 days
1800-1850 2385348.1 7.12 1.51 .162
1850-1900 2407048.1 8.42 1.55 .162
1900-1950 2433235.4 8.73 1.57 .175
1950-2000 2445437.8 8.68 1.47 .171
2000-2050 2454206.9 8.64 1.34 .149
Earth
sampling interval = 2.625 days
1800-1850 2382404.8 13.76 1.21 .188
1850-1900 2407612.6 15.22 1.21 .175
1900-1950 2419246.6 14.97 1.19 .219
1950-2000 2436779.0 12.15 1.18 .182
2000-2050 2469371.0 14.74 1.08 .184
Moon (geocentric)
sampling interval = 0.875 day
1800-1850 2384411.1 20.69 10.52 .00296
1850-1900 2406647.5 19.08 11.28 .00289
1900-1950 2419433.9 20.31 11.24 .00297
1950-2000 2445775.7 18.77 9.26 .00287
2000-2050 2467572.0 22.03 11.43 .00286
Mars
sampling interval = 0.875 day
1800-1850 2382804.6 18.64 2.84 .850
1850-1900 2398578.2 18.40 3.28 .879
1900-1950 2421995.0 15.62 2.72 .875
sampling interval = 9.875 days
1950-2000 2447472.9 18.21 2.32 .815
2000-2050 2452193.1 19.15 2.36 .888
Jupiter
sampling interval = 9.875 days
1800-1850 2388150.1 34.99 6.04 4.24
1850-1900 2409845.5 28.34 5.35 3.66
1900-1950 2417202.4 35.05 5.40 4.46
1950-2000 2451014.4 31.75 6.43 4.67
2000-2050 2460691.9 28.70 6.67 3.84
Saturn
sampling interval = 9.875 days
1800-1850 2387705.8 119.0 7.69 25.7
1850-1900 2409499.9 150.1 8.94 20.8
1900-1950 2431274.2 133.8 8.54 25.0
1950-2000 2439500.1 129.6 5.12 22.2
2000-2050 2468384.5 108.2 6.24 24.0
Uranus
sampling interval = 19.875 days
1800-1850 2378819.4 35.05 4.80 22.1
1850-1900 2400125.4 33.77 3.37 16.8
1900-1950 2430335.4 26.01 3.26 19.7
1950-2000 2435264.4 37.96 6.60 15.8
2000-2050 2469807.1 15.35 4.48 20.2
Neptune
sampling interval = 19.875 days
1800-1850 2396269.6 12.70 2.63 7.07
1850-1900 2407618.3 12.26 1.76 5.65
1900-1950 2418629.0 8.57 3.36 7.45
1950-2000 2451542.0 21.71 2.90 9.24
2000-2050 2454940.6 26.14 2.90 6.90