### Abstract

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.

Original language | English |
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Pages (from-to) | 1195-1204 |

Number of pages | 10 |

Journal | Advances in the Astronautical Sciences |

Volume | 99 |

Issue number | 2 |

Publication status | Published - 1998 |

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

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## Cite this

*Advances in the Astronautical Sciences*,

*99*(2), 1195-1204.