Optimal deflection of Earth-approaching asteroids

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 Earth-approaching object detection and possible interdiction. One method suggested for the prevention of the collision of an asteroid with the Earth is to deflect it from its course, perhaps using the explosion of a nuclear weapon. Solving the optimal control problem to maximize explicitly the resulting miss distance of the asteroid is problematic. A two-stage approach is used in this work. The time to interception, for a given interceptor launch date, is first minimized, that is, the time-optimal interception trajectory is found. Then at the time of interception the system state transition matrix is used to indicate the direction in which an impulse should be applied to the asteroid to maximize the subsequent deflection. This should in principle yield nearly the optimal deflection. Results are presented for the case of deflection of a real Earth-approaching asteroid, 1991 RB.