| Abstract: |
| Binary asteroids of nearly equal mass are rare, the fourth pair 2017 YE5 being discovered in 2017. A four-body problem we propose bridges the familiar restricted three-body problem, that is traditionally used to model the motion of single asteroids, and the more general four-body problem. This four-body problem allows the gravitational interaction of the asteroids in a binary pair, of any mass ratio, along with the gravitational interaction of two primaries. We show in the equal primary mass and in equal binary asteroid mass case the analytic existence of relative equilibria and periodic orbits, some near the Eulerian type relative equilibria, and some of Hill type where asteroid orbits a distinct primary. We also show in the case of equal primary mass and nearly equal binary asteroid masses the analytic existence of comet-like periodic orbits. |
|