PROPOSING TWO SPACE BASES AT L1 AND L3 (EARTH-MOON) FOR PLANETARY DEFENSE

摘要

A system of two space bases housing missiles is proposed to achieve the Planetary Defense of the Earth against dangerous asteroids and comets. 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 L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth). We show that placing at L1 and L3 bases of missiles would cause those missiles to deflect the trajectory of asteroids by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that the confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. An additional remark is that the theory developed in this paper is just a beginning of a larger set of future research work. In fact, while in this paper we only develop: 1) The analytical Keplerian theory of the Optimal Planetary Defense achievable from the Earth-Moon Lagrangian Points L1 and L3; 2) The relevant, simplified version, when the arriving asteroid hyperbola is regarded as coinciding with its own asymptote, namely it is just a straight line. The confocal missile trajectories orthogonal to this straight line cease then to be ellipses and are just circles centered at the Earth. This situation we call the straight line - circle approximation. 3) In the straight line - circle approximation, we are able to derive an important formula expressing the missile's final, increased speed just prior to hitting the asteroid in terms of the asteroid's speed, size and (presumed) density. This new, original equation is the key to understand which missile can deflect which asteroid far enough from the Earth surface. Yet, much more sophisticated analytical refinements would be needed to: 1) Take into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3; 2) Add more (non-optimal) trajectories of missiles shot from either the Lagrangian Points L4 and L5 of the Earth-Moon System or from the surface of the Moon itself; 3) Encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see "which asteroids could be diverted by which missiles", even in the very simplified scheme outlined here. Outlined for the first time in February 2002, our Confocal Planetary Defense concept is a Keplerian Theory that proved simple enough to catch the attention of scholars, representatives of the US Military and popular writers. These developments could possibly mark the beginning of an "all embracing" mathematical vision of Planetary Defense beyond all learned activities, dramatic movies and unknown military plans covered by secret.