Periodic Orbits Above the Ecliptic in the Solar-Sail Restricted Three-Body Problem

Abstract

We consider periodic orbits in the circular restricted three-body problem, where the third (small) body is a solar
\nsail. In particular, we consider orbits about equilibrium points in the Earth–sun rotating frame, which are high above
\nthe ecliptic plane, in contrast to the classical “halo” orbits about the collinear equilibria. It is found that due to
\ncoupling in the equations of motion, periodic orbits about equilibria are naturally present at linear order. Using the
\nmethod of Lindstedt–Poincaré, we construct nth order approximations to periodic solutions of the nonlinear
\nequations of motion. It is found that there is much freedom in specifying the position and period/amplitude of the
\norbit of the sail, high above the ecliptic and looking down on the Earth. A particular use of such solutions is presented,
\nnamely, the year-round constant imaging of, and communication with, the poles. We find that these orbits present a
\nsignificant improvement on the position of the sail when viewed from the Earth, compared to a sail placed at
\nequilibrium.