Mars crossers in the middle belt

Initial population of 158 main-belt asteroids with a = 2.5 - 2.8 AU, R = 0.2, 1, 2 and 5 km, C-type. Numerical integrations spanning 100 Myr, comparsion with runs without Yarkovsky effect.

- mean a(t) and proper (a, e) plots for runs a25-* - format GIF.
- proper (a, e) images in PS for whole groups of 4 runs.

1. criterion q < 1.665 AU: TP is classified as MC, when its (mean or proper) perihelion distance becomes smaller than 1.665 AU.
2. MC criterion: Heliocentric distance of TP along the intersection line of TP and Mars orbital planes have to be smaller than heliocentric distance of Mars in the same direction. The criterion uses mean elements of TP and also Mars, including their angles I, omega, Omega.
3. improved MC criterion: Additionaly to the "MC criterion", we distingiuish intersection points in the Mars orbital plane and we also enlarged Mars orbit by its Hill sphere. Finally we should use this improved MC criterion and mean elements (usual dt = ~432 yr). The algorithm is implemented in mc3.f program.

The slopes for criteria MC, improved MC and q < 1.665 AU are very similar, the main difference arises from initial fast decay during first ~1 Myr (secular cycle).

The curve describing improved MC criterion is always ABOVE the old MC-criterion, as we expected.

TPs were initially divided into 2 groups: "_mc" (69 TPs which became MC after 100 Myr without Yarkovsky effect) and the rest "_nomc" (89 TPs). In the following table are listed numbers of Mars crossers with respect to these groups for different asteroids radii and comparsion with no-Yarkovsky run.

We use different MC criterion (and different filtering) than in previous case, what may explain the difference in run a25-noya without Yarkovsky - there should be 69 _mc and zero _nomc, but this was NOT tested, because we do not know details on the initial splitting procedure.

However, the "q < 1.665 AU" criterion (and mean elements with dt = 432 yr) gives values 48 _mc and 21 _nomc for the same run. Notice the sum of both groups is equal 69, what corresponds to the total number of _mc particles - asteroids might only be "redistributed" between these two groups. (One of possible reasons are noisy mean elements due to anti-aliasing problem in filtering subroutines?)

Yarkovsky force does NOT decrease number of MC, which became MC already without Yarkovsky. One could see significant increse (>10 %) of MC only for the smallest bodies R = 200 m.

Particle no. 29 - capture in g-2g₆ +g₅ and z₁ resonances, images proper (a, e) and libration of critical angle, see also slides presented at NATO ASI (Blair Atholl, Jul 23rd-Aug 5th 2000)