The capture of small near-Earth asteroids in a bound binary pair in Earth's orbit

Abstract

Hill's approximation models the motion of two small masses gravitationally interacting with each other and perturbed by a large central body. An application of the model is employed in this paper to manoeuvre the relative motion of two asteroids by a small impulse to capture them in bound binary motion in Earth's orbit. The initial conditions prior to the capture manoeuvre are restricted in a parameter space termed the gateway region. The gateway region is produced by applying the constraint that the capture impulse is a real-valued function, and the zero-velocity curve closes, enveloping both asteroids. A full mission scenario is designed with three impulses. The first impulse transfers one asteroid from a far field region to the gateway region, where there is mutual interaction with the second asteroid, which is assumed to be the origin of the relative motion. The second impulse changes the trajectory of the asteroid in the gateway region to a linear drift approaching the second asteroid. The third impulse is calculated by means of increasing the Jacobi integral to reach the critical value required to close the zero-velocity curve. It is demonstrated in principle that the triple impulses enable the candidate asteroids to be captured in a bound pair in Earth's orbit. It is also shown that the thruster on-time for the capture impulse as applied for the different small asteroids considered is short relative to the natural time-scale of the orbital dynamics of the problem, which shows the feasibility of the impulse approximation with the typical thruster forces applied. This strategy could provide a basis for parking small captured near-Earth asteroids in Earth's orbit.