Optimal Low-Thrust Interception of Earth-Crossing Asteroids

Abstract

The spectacular collision of the Shoemaker–Levy 9 asteroid with Jupiter in July 1994 was a dramatic reminder of the inevitability of such catastrophes in the Earth’s future unless steps are taken to develop methods for Earthapproaching object detection and possible interdiction. In this work, optimal (minimum-time) trajectories are determined for the interception of asteroids that pose a threat of collision with the Earth. An impulsive-thrust escape from the Earth is used initially to reduce  ight time but is followed with continuous low-thrust propulsion using values of thrust and speciŽ c impulse representative of electric motors. The continuous optimization problem is formulatedas a nonlinearprogrammingproblemusing the collocationmethod inwhich thedifferential equations of motion are included as nonlinear constraint equations. The use of low-thrust propulsion after Earth escape is shown to dramatically decrease the mass of the interceptor vehicle at launch.