The Kirkwood gaps in the asteroid belt occur where an asteroid's orbital period is a…
PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Astrophysics & Cosmology · Celestial mechanics and planetary systems
Action and Symmetry, Ch Perturbed orbits, precession and the three-body problem
Problem
The Kirkwood gaps in the asteroid belt occur where an asteroid's orbital period is a simple ratio of Jupiter's, so that repeated tugs from Jupiter accumulate through a small denominator. Jupiter's semi-major axis is aJ=5.2038AU. Using Kepler's third law, find the semi-major axis, in AU, of the 4:1 mean-motion resonance with Jupiter, at which an asteroid completes four orbits for every one of Jupiter's.