Calcul de la distance minimale entre l'orbite de la Terre et celle d'un astéroïde proche de celle-ci

Abstract

Basing our work on a chapter of Dr. G-F Gronchi's thesis, we are interested in the problem of a possibility of a collision between the Earth and a NEA (a Near earth Asteroid) by compute the minimal distance between their respective orbit. So, we are concerned about the compute of the angular position that should have two bodies which cover an elliptic orbit with a common focus, so that the distance between them be minimal. In that order, we study the stationnary points of the squared distance d2 between a point on an ellipse and a point on the second one. First, we are interested in the mathematical problem of giving an upper bound of the number of stationnaty points of d2 and establishing when they are infinitely many, this problem is the biggest part of our work and uses the D.N. Berstein's theorem. We propose then, a method which allows to compute all the stationnaly points as well as their singularity, this method relies on the algebraic theory of the resultant. We finally introduce some results given by G-F Gronchi in the case earth-asteroid.

Date of Award	2004
Original language	French
Supervisor	Florent Deleflie (Jury), Sylvie Jancart (Jury) & Anne Lemaitre (Supervisor)