Régularisation de la distance minimale entre deux orbites: application aux impacteurs virtuels

Abstract

This memoir is based on articles (Gronchi G.F., 2005) and (Gronchi D.F. et Tommei G., 2007) dealing with the minimal distance between two confocal Keplerian orbits. In the first part, the problem is posed: computing the angular positions of the bodies covering the two orbits in such a way that the distance from each other is minimal. Next, an algorithm solving this problem which uses the theory of the resultant and the fast Fourier transform is presented. We have implemented it in matlab and some results obtained by this program are shown. The second part is devoted to probe the uncertainty of our results. At first, the problem is generalized to various orbital elements to avoid undefined elements. A procedure computing the uncertainty of th distance which is based on Gauss'method is then presented. We also build up a regularized distance function which eliminates the problems caused by the non-differentiability and by the constraint on the sign of the distance. Finally, the theory seen in this second part is applied to the research of virtual potentialy hasardous asteroids.

Date of Award	2007
Original language	French
Supervisor	Anne Lemaitre (Supervisor), Timoteo Carletti (Jury) & Jacques HENRARD (Jury)