The gravitational effects of Earth in calculating optimal impulses for deflecting Earth-crossing asteroids are presented in this paper. The patched conic method is used to formulate a constrained optimization problem. The constraints at Earth are pulled back to the constraints at the edge of the sphere-of-influence. The result is a modified heliocentric two-body optimization problem with first-order constraints. Numerical solutions to this approximate three-body problem indicate that the delta-V requirements are considerably more than that obtained by a pure two-body analysis. Generally speaking, the increments in the minimum delta-V due to the gravitational effects of Earth are large (by as much as 60%) for near-Earth asteroids, and the errors diminish for asteroids with large (i.e. e > 0.7) eccentricities.
|Number of pages||10|
|Journal||Advances in the Astronautical Sciences|
|Publication status||Published - 1998 Dec 1|
All Science Journal Classification (ASJC) codes
- Aerospace Engineering
- Space and Planetary Science