The longitudes of planets are given as mean geocentric longitudes
for the mean equinox of date (EOD) (movable astrology) or for the reference equinox of zero date (fixed astrology).
Correction UT-ET is taken into account.
Low-precision ephemeris
Formulae are from an article from
The astrophysical Journal Supplement, 41.391-411 November 1979
Low-precision formulae for planetary positions
The reader can refer to the file nph-iarticle_query.pdf in the docs directory of Proastro.
The advantage of this method is its speed, inconvenience is that it is not possible to go more than +/- 300 years from 1979
(according to the authors) having the precision of one arc minute for the longitudes of planets.
Tests show the following differences between JPL DE406 and the article of the astrophysical journal
for 1200 after J.C.
Sun : | about 1 minute of arc degree |
Moon : | 10 minutes of arc degree |
Mercury : | about 1 minute of arc |
Venus : | about 2 minutes of arc |
Mars : | about 2 minutes |
Jupiter : | about 1 minute |
Saturn : | about 1 minute |
Uranus : | about 10 seconds of arc |
Neptune : | about 10 minutes of arc |
Pluto : | about 2 degrees (!) |
You can test it yourself by calculating a card, then "Recompute the horoscope" having changed Ephemeris used in menu "Options / Ephemeris."
Internal ephemeris
This is a truncated version of BDLFM091 from French "Bureau des longitudes", now "IMCCE". The accuracy is nearly the same as
the JPL high accuracy Ephemerides DE406, except for the moon (40 arc minutes difference for 3000 BC date) and for Pluto (4 degrees for 3000 BC).
The advantage of this method is that the binary file of 190 Mb
is not necessary and one can extend beyond 3000 BC to 3000 AC limits.
Inconvenience is a longer calculation time (several thousand sinus per horoscope card)
For dates from 13000 BC to 17000 AC, it's better to use binary file DE431 from JPL
The ephemerides of Pluto do not come from the IMCCE.
Ephemeris high accuracy DE406 from Jet Propulsion Laboratory
Accuracy is "exact" for interval -3000 to 3000
A binary file UNIX.406 of about 190 Mb is required
This file is not free, and must be bought here:
http://www.willbell.com/SOFTWARE/jpl.htm
Update May 2021: File DE406 can be downloaded for free here:
ftp://ssd.jpl.nasa.gov/pub/eph/planets/Linux/de406/lnxm3000p3000.406
Accuracy is "exact" for interval -13000 to +17000
A binary file (lnxm13000p17000.431) of 2.7 Go is required
This file is free, and can be downloaded here:
ftp://ssd.jpl.nasa.gov/pub/eph/planets/Linux/de431/lnxm13000p17000.431
Remark: In previous version of Proastro it was necessary to translate UNIX.406 or other JPL binaries from "big endian" to "little endian"
This stage is not required any more, translation "big endian" to "little endian" is automatically done, if needed.
Performances:
The best performances are obtained with ephemeris DE406
who only need file of about 200 Mb.
Low precision ephemeris are less fast than DE406 but does not need the binary file DE406.
DE431 must be used for astronomical charts in far past but asks a big file of 2.7 Go.
However performances are little affected in comparison with DE406.
To compare with the ephemerides in Proastro, you have two websites:
See also: