Guiding Asteroids to Form an Artificial Binary System Using Continuous Control Acceleration

Asteroids are being considered for future science missions and for resource exploitation. This paper investigates whether low-thrust acceleration may control two asteroids’ trajectories to form a bounded binary asteroid system inside their zero-velocity curve. An analytical method models an active transverse control acceleration between two asteroids on adjacent circular orbits as a constant or exponential function of transverse position to ensure that the binary asteroid system’s Jacobi constant achieves a critical value. Hill’s equations are modified to include the continuous control acceleration, which is disabled when the asteroid crosses the radial axis, between the two collinear Lagrange equilibrium points. The hypothetical scenario in the Earth-Moon system involves two small, equal-sized spherical asteroids encountering each other on circular orbits. The solution simulation shows that the zero-velocity curve can encompass the two bound asteroids after turning off the control acceleration. The variable-order Gaussian quadrature collocation approach in the general-purpose MATLAB optimization tool GPOPS-II was also used by specifying different boundary conditions to verify the accuracy of the reference solution, and to extended and the problem to find the optimum minimum-time solutions. Allowing the control acceleration direction to vary yielded an optimal solution that decreases the final time. The propellant mass was calculated using the BepiColombo thruster specific impulse and the optimum solution’s velocity change. The propellant mass is found to be low due to the low relative speed of the asteroids. • A continuous acceleration control law enables bound motion of an asteroid pair. • Hill’s equations are modified with constant or exponential transverse control acceleration terms. • Contact between the asteroids is considered a potential endpoint of the capture. • GPOPS-II refines a reference solution with optimal final time and thrust steering. • Required propellant mass is modest for the small asteroids considered.