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 are of order
10-4 AU.
 |
 |
| 2953-cp0 |
2953-cp1 |
The calculation using swift_bs (Burlisch-Stoer) integrator with the same
initial conditions (2953-cp0bsf).
The time span 20 Myr is shorter than in previous cases
due to the much slower integrator. Jumps in a are even smaller then
10-4 AU.
We also started the run with only three most interesting test particles
(2953-cp2bsf) and one can see their evolution upto 100 Myr.
 |
 |
| 2953-cp0bsf |
2953-cp2bsf |
Analysis of the jumps (Are they caused by close encouters with Ceres or Pallas
or interactions with weak resonances, e. g. 9J-10S-2 located in this region?):
- t = 5.1393 Myr,
da = 5 × 10-4 AU
<= the close encounter with Ceres,
minimal separation 2.50 × 10-4 AU
- t = 68.1936 Myr,
da = 0.001 AU
due to the encounter with Ceres
at the distance only 1.11 × 10-4 AU
Miroslav Broz,
miroslav.broz@email.cz,
Apr 21st 2000