A three million year integration of the earth's orbit

Abstract

The equations of motion of the nine planets and the spin axis of the earth are integrated for 3.05 million years into the past. The initial conditions are taken from the JPL DE 102 ephemeris; dominant relativistic corrections and corrections for the earth-moon system's quadrupole moment are included; but solar mass loss is not considered. A low-pass filter is employed to remove short-term variations and isolate variations of more than 2000 years. At the end of integration, the fractional error in the earth's position is shown to be less than 0.03 radian, and larger errors of up to several radians are shown for other planets. Because the adjacent trajectories do not diverge exponentially, the planetary orbits are apparently regular. Between 1 and 2 Myr in the past, a burst of oscillations are found in the semimajor axes of Venus and the earth. The results are compared to other models, and disagreement is shown between the results of secular perturbation theory and this model's predictions beyond 1-1.5 Myr into the past.