Inner Planets

We consider first the inner planets. The greatest differences, and thus the greatest corrections, are for the period prior to -1349. The maximum range of uncorrected and corrected differences AE - DE406 that appear in our comparisons (which may not be complete) for geocentric  coordinates to the nearest 0.1 units is as follows:

 

Planet

Period of correction

Uncorrected differences (period of correction)
Corrected differences (entire ephemeris)

longitude
(seconds)

latitude
(seconds)

distance
(10-6 AU)

Mercury

-2999 to -1349
corrected

-4.0 to 11.0
-0.9 to 0.8

-2.6 to 2.5
-0.5 to 1.0

-21.5 to 29.0
-1.8 to 1.9

Venus

uncorrected
corr. from Earth

-9.6 to 11.3
-2.5 to 1.0

-1.7 to 3.6
-1.0 to 2.9

-21.1 to 15.5
-5.8 to 4.5

Sun

-2999 to -1349
corrected

-2.7 to 5.9
-0.4 to 0.6

not given

-9.6 to 9.8
-0.6 to 0.7

Mars

-2999 to +300
corrected

-0.6 to 1956
-1.0 to 3.6

-67.0 to 29.4
-0.8 to 2.3

-3073 to 3113
-4.4 to 5.5

 

The corrections were made in a way that is computationally intensive but appears to work satisfactorily. For Mercury, Earth, Mars, and Pluto a table was computed of the differences DE406 - AE of heliocentric coordinates for the specified periods, at intervals of 10 days for Mercury, 30 days for the Earth and Mars, and 2130 days for Pluto. This table appears as the file 'correction.dat'. For dates within the range of correction, AE looks up corrections in the table and adds them to the uncorrected heliocentric coordinates; the corrected heliocentric coordinates then appear in the ephemeris and in turn are used to compute the corrected geocentric coordinates. For Mercury, Mars, and Pluto there are corrections for heliocentric longitude, latitude, and distance; for the earth heliocentric latitude is omitted; no corrections were required for Venus.

Alcyone Ephemeris Documentation
(C) 2007 Alcyone Software