 Asteroid belt

The main asteroid belt is a population of asteroids and other Small Solar System body objects orbiting chiefly between Mars and Jupiter. Its members occupy many separate orbits, rather than forming a solid ring. Their orbital distribution records both the history of planet formation and continuing gravitational perturbations.

A particularly clear observation is the series of Kirkwood gaps, deficits in asteroid counts at certain semi-major axes. The JPL Solar System Dynamics histogram, constructed in June 2007 from 156,929 numbered asteroids with well-determined orbits, shows gaps associated with mean-motion resonances with Jupiter.^[ref]

For the $3:1$ resonance, an asteroid makes three revolutions during one Jovian revolution, so $T_a=T_J/3$. Using Kepler's third law and Jupiter's semimajor axis of about $5.20$ astronomical units givesRepeated gravitational forcing can change orbital elements and remove bodies from parts of this region. A resonance label specifies the ratio of orbital frequencies here, so reversing it into a period ratio would give the wrong location. The histogram shows the observed distribution under a stated selection, rather than a complete census of every small asteroid.