Symmetric comet-type periodic orbits in the elliptic three-dimensional restricted (N+1)-body problem

Abstract

For $N\ge 3$, we show the existence of symmetric periodic orbits of very large radii in the elliptic three-dimensional restricted $(N+1)$-body problem when the $N$ primaries have equal masses and are arranged in a $N$-gon central configuration. These periodic orbits are close to very large circular Keplerian orbits lying nearly a plane perpendicular to that of the primaries. They exist for a discrete sequence of values of the mean motion, no matter the value of the eccentricity of the primaries.