Astronomy
Jupiter’s resonance clock
Thousands of asteroids integrated under an eccentric Jupiter: the resonances pump their eccentricities until the orbits cross Mars or Jupiter, and the gaps open by themselves. Make Jupiter heavier to watch it happen within the run.
The model and its limits
The planar elliptic restricted problem: the Sun and Jupiter only, Jupiter on a fixed ellipse, no Saturn, no secular resonances, no Mars or Earth beyond the removal rule. The accelerator is Jupiter’s mass; the real clearing took millions of years. The P:Q ring is the Keplerian locator of ring 2.
Equations used in the module
Equations a_res = a_J(q/p)^(2/3); T ∝ a^(3/2); T_syn = 1/|1/T - 1/T_J| integrated: a = −GM r/r³ − Gm (r − r_J)/|r − r_J|³ − Gm r_J/r_J³; removed when q < 1.52 AU or Q > 0.94 a_J
