4. Technical details
The numerical integrations for the BCP model have been performed using a Taylor method of order 20 (Jorba & Zou 2000). The numerical integrations for the JPL model have been carried out by a standard Runge-Kutta-Fehlberg method of orders 7 and 8. A sample of the results has been tested -on a different computer- against a third numerical integrator, the Shampine-Gordon method (Shampine & Gordon 1975). The results obtained are quite similar, with very small differences that seem to come from the different arithmetic and truncation errors.
The numerical integrations for the JPL model have been performed as follows. From the data in the JPL ephemeris file, we compute the equatorial coordinates of each planet (with origin at the instantaneous centre of mass of the Solar system), except for the Moon whose coordinates are referred to the Earth. From a numerical point of view, it is not a good idea to have the origin of coordinates at the centre of mass of the Solar system because then the different coordinates of the trajectories near the triangular points of the Earth-Moon system are very close, and this could result in cancellations of meaningful digits. For this reason, the origin of the coordinates has been translated to the Earth-Moon barycentre. The ideas for these tasks are described in Gómez et al. (1985; 1987; 1991; 1993).
© European Southern Observatory (ESO) 2000
Online publication: December 15, 2000