Annihilation of relative equilibria in the gravitational field of irregular-shaped minor celestial bodies

Abstract

The rotational speeds of irregular-shaped minor celestial bodies can be changed by the YORP effect. This variation in speed can make the numbers, positions, stabilities, and topological cases of the minor body's relative equilibrium points vary. The numbers of relative equilibrium points can be reduced through the collision and annihilation of relative equilibrium points, or increase through the creation and separation of relative equilibrium points. Here we develop a classification system of multiple annihilation behaviors of the equilibrium points for irregular-shaped minor celestial bodies. Most minor bodies have five equilibrium points; there are twice the number of annihilations per equilibrium point when the number of equilibrium points is between one and five. We present the detailed annihilation classifications for equilibria of objects which have five equilibrium points. Additionally, the annihilation classification for the seven equilibria of Kleopatra-shaped objects and the nine equilibria of Bennu-shaped objects are also discussed. Equilibria of different objects fall into different annihilation classifications. By letting the rotational speeds vary, we studied the annihilations and creations of relative equilibria in the gravitational field of ten minor bodies, including eight asteroids, one satellite of a planet, and one cometary nucleus: the asteroids were 216 Kleopatra, 243 Ida, 951 Gaspra, 1620 Geographos, 2063 Bacchus, 2867 Steins, 6489 Golevka, and 101955 Bennu; the satellite of the planet was S16 Prometheus; and the comet was 1682 Q1/Halley. For the asteroid 101955 Bennu, which has the largest number of equilibria among the known asteroids, we find that the equilibrium points with different indices approach each other as the rotational speed varies and thus annihilate each other successively. The equilibrium in the gravitational field and the smooth surface equilibrium collides when the equilibrium touches the surface of the body.