title: Optimal trajectories from the Earth-Moon L1 and L3 points to deflect hazardous asteroids and comets.
abstract: Software code named asteroff was recently created by the author to simulate the deflection of hazardous asteroids off of their collision course with the Earth. This code was both copyrighted and patented to avoid unauthorized use of ideas that could possibly be vital to construct a planetary defense system in the vicinity of the Earth. Having so said, the basic ideas and equations underlying the asteroff simulation code are openly described in this paper. A system of two space bases housing missiles is proposed to achieve the planetary defense of the Earth against dangerous asteroids and comets, collectively called impactors herein. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L(1) (between the Earth and the Moon) and L(3) (in the direction opposite to the Moon from the Earth). We show that placing missile bases at L(1) and L(3) would enable those missiles to deflect the trajectory of impactors by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. One additional remark is that the theory developed in this paper is just a beginning for a wider set of future research. In fact, we only develop the Keplerian analytical theory for the optimal planetary defense achievable from the Earth-Moon Lagrangian points L(1) and L(3). Much more sophisticated analytical refinements would be needed to: (1) take into account many perturbation forces of all kinds acting on both the impactors and missiles shot from L(1) and L(3); (2) add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L(4) and L(5) of the Earth-Moon System or from the surface of the Moon itself; and (3) encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see which impactors could be diverted by which missiles, even in the very simplified scheme outlined here. Published for the first time in February 2002, our Keplerian planetary defense theory has proved, in just one year, to be simple enough to catch the attention of scholars, in addition to popular writers, and even of someone from the US Military. These recent developments might possibly mark the beginning of an all embracing vision in planetary defense beyond all learned congressional activities, dramatic movies, and unknown military plans covered by secrecy.
authors.affiliation: International Academy of Astronautics, Torino, Italy.
authors.forename: Claudio
authors.initials: C
authors.lastname: Maccone