Collision and Annihilation of Relative Equilibrium Points Around Asteroids with a Changing Parameter

Abstract

In this work, we investigate the bifurcations of relative equilibria in the gravitational potential of asteroids. A theorem concerning a conserved quantity, which is about the eigenvalues and number of relative equilibria, is presented and proved. The conserved quantity can restrict the number of non-degenerate equilibria in the gravitational potential of an asteroid. It is concluded that the number of non-degenerate equilibria in the gravitational field of an asteroid varies in pairs and is an odd number. In addition, the conserved quantity can also restrict the kinds of bifurcations of relative equilibria in the gravitational potential of an asteroid when the parameter varies. Furthermore, studies have shown that there exist transcritical bifurcations, quasi-transcritical bifurcations, saddle-node bifurcations, saddle-saddle bifurcations, binary saddle-node bifurcations, supercritical pitchfork bifurcations, and subcritical pitchfork bifurcations for the relative equilibria in the gravitational potential of asteroids. It is found that for the asteroid 216 Kleopatra, when the rotation period varies as a parameter, the number of relative equilibria changes from 7 to 5 to 3 to 1, and the bifurcations for the relative equilibria are saddle-node bifurcations and saddle-saddle bifurcations.

25pages, 3 figures, accepted by MNRAS

References in corpus (6)

• Analysis of the Potential Field and Equilibrium Points of Irregular-shaped Minor Celestial Bodies
• Orbits and Manifolds near the Equilibrium Points around a Rotating Asteroid
• Topological Classifications and Bifurcations of Periodic Orbits in the Potential Field of Highly Irregular-shaped Celestial Bodies
• Analysis of Asteroid (216) Kleopatra using dynamical and structural constraints
• Equilibrium Points and Periodic Orbits in the Vicinity of Asteroids with an Application to 216 Kleopatra
• Orbital Mechanics near a Rotating Asteroid

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• Surface Dynamics, Equilibrium Points and Individual Lobes of the Kuiper Belt Object (486958) Arrokoth
• Dynamical Environment and Surface Characteristics of Asteroid (16) Psyche
• Stable Periodic Orbits for Spacecrafts around Minor Celestial Bodies
• Annihilation of Relative Equilibria in the Gravitational Field of Irregular-shaped Minor Celestial Bodies
• Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems
• Hamiltonian Formulation and Perturbations for Dust Motion around Cometary Nuclei
• Dynamical Environment in the Vicinity of Asteroids with an Application to 41 Daphne
• Dynamical Model of Binary Asteroid Systems Using Binary Octahedrons