Bifurcations of Periodic Orbits in the Gravitational Field of Irregular Bodies: Applications to Bennu and Steins

Abstract

We investigate the topological types and bifurcations of periodic orbits in the gravitational field of irregular bodies by the well-known two parameter analysis method. Results show that the topological types of periodic orbits are determined by the locations of these two parameters and that the bifurcation types correspond to their variation paths in the plane. Several new paths corresponding to doubling period bifurcations, tangent bifurcations and Neimark–Sacker bifurcations are discovered. Then, applications in detecting bifurcations of periodic orbits near asteroids 101955 Bennu and 2867 Steins are presented. It is found that tangent bifurcations may occur three times when continuing the vertical orbits near the equilibrium points of 101955 Bennu. The continuation stops as the Jacobi energy reaches a local maximum. However, while continuing the vertical orbits near the equilibrium points of 2867 Steins, the tangent bifurcation and pseudo period-doubling bifurcation occur. The continuation can always go on, and the orbit ultimately becomes nearly circular.

Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

“…The bifurcation of periodic orbit families helps locate points of extrema along the periodic orbit family with respect to the period or energy; such kinds of bifurcations are called first-kind bifurcations. The first kind of bifurcation of periodic orbit families around asteroids has been well studied in the literature [25][26][27]. Ni et al showed that multiple first-kind bifurcations occur along a periodic orbit family around an asteroid [28].…”

“…On the other hand, the literature has paid little attention to period-multiplying bifurcations around asteroids. Liu et al were able to locate period-doubling bifurcations around asteroids Bennu and Steins [26]. Brown and Scheeres located and computed period-multiplying bifurcations up to integer five around the asteroid Bennu [33].…”

“…Previous literature only studied tangent bifurcations of periodic orbits around asteroids (see [25][26][27][28][29]). Period-multiplying bifurcations of periodic orbit families around asteroids have only been gaining interest recently.…”