Feasibility of orbital capture of near-earth asteroids based on the planar-circular restricted three-body problem

Abstract

With the goal of efficiently extracting samples or even materials from the surface of an asteroid, this study proposed and investigated a method to change the velocity vector of a near-Earth asteroid and place it into an orbit where it is captured by the Earth’s gravitational field. The change in the orbit of an asteroid is not directly discussed in relation to the change in the velocity vector but is indirectly considered by the change in the Jacobi integral, which is the first integral of the circular-planar restricted three-body problem. In addition, the distribution of the smaller alignment index (SALI) is investigated to find a capture point where the asteroid is not put into a chaotic orbit. The proposed method is numerically demonstrated for fictional asteroid capture missions. The results show that several asteroids can be put into stable captured orbits. Additionally, we propose a method to optimize the value of the Jacobi integral, aiming to stabilize periodic captured orbits. Numerical integration confirms that when the Jacobi integral is optimized, the orbital lifetime of the captured orbit exceeds 500 years.