Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

Abstract

Periodic orbit families around asteroids serve as potential trajectories for space probes, mining facilities, and deep space stations. Bifurcations of these families provide additional candidate orbits for efficient trajectory design around asteroids. While various bifurcations of periodic orbit families around asteroids have been extensively studied, period-multiplying bifurcations have received less attention. This paper focuses on studying period-multiplying bifurcations of periodic orbit families around asteroids. In particular, orbits with periods of approximately 7 and 17 times that of the rotational period of asteroid 216 Kleopatra were computed. The computation of high-period orbits provides insights into the numerical aspects of simulating long-duration trajectories around asteroids. The previous literature uses single-shooting and multiple-shooting methods to compute bifurcations of periodic orbit families around asteroids. Computational difficulties were encountered while using the shooting methods to obtain period-multiplying bifurcations of periodic orbit families around asteroids. This work used the Legendre–Gauss collocation method to compute period-multiplying bifurcations around asteroids. This study recommends the use of collocation methods to obtain long-duration orbits around asteroids when computational difficulties are encountered while using shooting methods.