Keplerian orbits with a common focus and secular evolution in the R3BP with crossing singularities
Giovanni Federico Gronchi (Università di Pisa)
Mercredi 8 mars, 11h, en ligne (lien zoom).
Abstract. “The computation of the distance dmin between two Keplerian trajectories A, A‘ with a common focus, also called MOID or orbit distance, is relevant for different purposes in Celestial Mechanics. Several authors introduced efficient methods to compute dmin. Small values of dmin are relevant for the assessment of the hazard of near-Earth asteroids (NEAs) with the Earth or for the detection of conjunctions between satellites of the Earth.
In this talk we review some results concerning the computation of dmin and of its uncertainty, making an analysis of the singularities of the orbit distance.
Moreover, we shall deal with the long term behaviour of the solutions of the restricted three-body problem, say Sun-Earth-asteroid, when the osculating Keplerian trajectory of the asteroid can cross the trajectory of the Earth.
Crossings of trajectories (occurring when dmin =0) correspond to singularities of the averaged Hamilton equations, where the average is made over the two fast Delaunay variables of the asteroid and the Earth. We can define piecewise differentiable solutions of the averaged equations and show that the secular evolution of dmin is more regular than the one of the orbital elements.”
