Abstract:
We study the evolution of asteroid orbits in a restricted threebody problem formulation consisting of the Sun, the planet Jupiter and an unspecified asteroid of negligible mass. It was discovered by Kirkwood that the distribution of asteroid orbits contains gaps for orbits whose period is commensurate with that of Jupiter. Detailed computations in three-dimensional, many-body formulations found that test bodies initially placed in a forbidden orbit did not develop large eccentricities or leave the gap even after the passage of 10^5 years. In the present two-dimensional simulation, an extension of earlier work, we perform numerical integrations of the coupled equations of motion for Jupiter and the asteroid. Under assumptions of a stationary Sun and a circular orbit for Jupiter, we find that test bodies initially placed in a forbidden orbit can develop a large eccentricity after relatively few orbits.
