Gravitational Effects of Earth in Optimizing Delta V for Deflecting Earth-Crossing Asteroids

Abstract

Analyses incorporating the gravitational effects of Earth to calculate optimal impulses for deflecting Earth-crossing asteroids are presented. The patched conic method is used to formulate the constrained optimization problem. Geocentric constraints are mapped to heliocentric variables by the use of the impact parameter. The result is a unified nonlinear programming problem in the sense that no distinctions are made for short or long warning times. Numerical solutions indicate that the delta V requirements are considerably more than those of the previously published two-body analysis that excluded third-body effects. Generally speaking, the increments in the minimum delta V due to the gravitational effects of the Earth are large (by as much as 60%) for near-Earth asteroids, and the errors diminish for orbits with large eccentricities (e>0.7). Some interesting results for short warning times are also discussed.