Long Term Dynamics of the Outer Solar System Review of Longstop Project

Abstract

Project LONGSTOP was set up to investigate the long term dynamics of the outer solar system over timescales comparable to its age. This was done by means of numerical integrations on a CRAY-1S computer. Comparison with analytic theories required the use of filtering procedures and Fourier analysis. The 6-body point-mass newtonian problem, plus a gaussian ring model for the effect of the inner planets, turned out to be a good approximation to the real system; general relativity corrections can be easily introduced although they are not yet critical over 100 Myr. Long term variations in shape and orientation of planetary orbits from numerical integrations over 9.3 Myr suggested that analytic theories must be improved in order to be valid for such a timespan. Variations in the major semiaxes of Uranus and Neptune with a 1.119 Myr period have been found in the data; they could be recovered also analytically once the amplifying effect of the 2/1 quasi-resonance in mean motion between Uranus and Neptune was taken into account. The 100 Myr integration LONGSTOP 1B revealed the presence of a very small divisor with 31 Myr period. In relation with this small divisor, and with others which could not be identified with combinations of up to 8 fundamental frequencies, there appeared to be an accumulation of spectral lines of comparable amplitude in some regions of the spectrum. This was not the case when the output of the 9.3 Myr integration LONGSTOP 1A was analyzed; it suggests that 100 Myr might be long enough a timespan already to reveal the presence of non regular regions of motion in the phase space.