Gravitational effects of Earth in optimizing Delta V for deflecting Earth-crossing asteroids

Analyses incorporating the gravitational effects of Earth to calculate opti mal impulses for deflecting Earth-crossing asteroids are presented. The pat ched 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 proble m in the sense that no distinctions are made for short or long warning time s. Numerical solutions indicate that the DeltaV requirements are considerab ly more than those of the previously published two-body analysis that exclu ded third-body effects. Generally speaking, the increments in the minimum D eltaV due to the gravitational effects of the Earth are large (by as much a s 60%) for near-Earth asteroids, and the errors diminish for orbits with la rge eccentricities (e > 0.7). Some interesting results for short warning ti mes are also discussed.