Ceres, Pallas encounters

The effect of close encounters between test particles and massive bodies strongly affects the stability of swift_rmvs3 integrator. In the first test run (2953-cp0) we used time step 36 days and RHSCALE = 7 (only for Ceres and Pallas). This lead to approximately 1000 encounters closer than (RHSCALE * Hill sphere radius) within 100 Myr. The jumps in a thus occur very frequently and the overall amplitude of semimajor axis might be upto 10-3 AU.

The time step and RHSCALE was decreased in the second run (2953-cp1): dt = 2 days, RHSCALE = 1. The number of encounters within the Hill sphere decreased downto 1 or 10, as we expected. The most of a changes due to encounters is of order 10-4.

a(t) graphs for 2953-cp0 and 2953-cp1 runs (images 2953-cp0-a.gif, 2953-cp1-a.gif).

The calculation using swift_bs (Burlisch-Stoer) integrator with the same initial conditions. The time span is much shorter than in previous cases (<= slower integrator). Jump in a are smaller then

a(t) graph for 2953-cp0bsf run (image 2953-cp0bsf-a.gif).

Miroslav Broz, miroslav.broz@email.cz, Nov 26th 1999