Analytical and numerical results on families of n-ejection-collision orbits in the RTBP

Abstract

In the planar RTBP with mass ratio µ we regularise the singularity at one of the primaries by means of Levi-Civita’s transformation in a rotating frame. We solve the variational equations in a neighbourhood of the ejection/collision orbits, giving analytic expressions for the first terms in µ of the convergent expansion for orbits with eccentricity e¿¿¿1. For high enough values of the Jacobi constant C we give analytic expressions for the coefficients of the above expansion in powers of the small parameter and we prove the existence of four families of the so called n-ejection-collision (EC) orbits, that are orbits which eject from the primary and reach n relative maxima in the distance with the primary before finally colliding with it. Moreover, massive numerical explorations extending the analytical result for any value of the mass ratio and bigger ranges of C are also shown and discussed.