Asteroid belt gravity - 2D top view

Hundreds of massless asteroids orbit the Sun while Jupiter stirs them; resonances show up in the histogram.

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System

Exaggerating Jupiter speeds up what would take millennia.

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The science

Restricted three-body problem

Each asteroid obeys r̈ = -GM r/r³ + GMJ [(rJ - r)/|rJ - r|³ - rJ/rJ³] with Jupiter on a circular 5.2 AU orbit (indirect term included). A kick-drift-kick leapfrog with a 0.02 yr step keeps the energy of an isolated orbit stable.

Resonances

An asteroid whose period is TJ p/q meets Jupiter at the same orbital phase again and again and is pumped to large eccentricity. Kepler's third law T² = a³ places these at a = aJ (q/p)2/3: 2.50 AU for 3:1, 2.82 AU for 5:2, 2.96 AU for 7:3 and 3.27 AU for 2:1 (the Kirkwood gaps).

Honest simplifications: two dimensions, circular Jupiter, no Mars, Saturn or Yarkovsky drift, 2-3 orders of magnitude fewer bodies than the real belt. Real gaps need about 105 years or more at real Jupiter mass, so the slider exaggerates the mass; heavy settings mostly scatter the outer belt rather than reproduce the exact gap pattern.

What to try
  • Tick the rotating frame: horseshoe and resonant families become static shapes.
  • Run Strong Jupiter (x20) and watch the outer belt thin out and the mean eccentricity climb.
  • Pick No Jupiter: nothing changes, proving the stirring comes from Jupiter alone.
Number of asteroids vs semi-major axis
Eccentricity vs semi-major axis
Mean eccentricity over time