Thomas Waters

Control of solar sail periodic orbits in the elliptic three-body problem

A solar sail essentially consists of a large mirror that uses the momentum change due to photons reflecting off the sail for its impulse. Solar sails are therefore unique spacecraft, as they do not require fuel for propulsion [1]. In this Note we consider using the solar sail to continuously maintain a periodic orbit above the ecliptic plane using variations in the sails orientation. Positioning a spacecraft continuously above the ecliptic would allow continuous observation and communication with the poles.

Invariant manifolds and orbit control in the solar sail three-body problem

In this paper, we consider issues regarding the control and orbit transfer of solar sails in the circular restricted Earth-sun system. Fixed points for solar sails in this system have the linear dynamic properties of saddles crossed with centers; thus, the fixed points are dynamically unstable and control is required. A natural mechanism of control presents itself: variations in the sails orientation. We describe an optimal controller to control the sail onto fixed points and periodic orbits about fixed points. We find this controller to be very robust, and we define sets of initial data using spherical coordinates to get a sense of the domain of controllability; we also perform a series of tests for control onto periodic orbits. We then present some mission strategies involving transfers from the Earth to fixed points and onto periodic orbits and involving controlled heteroclinic transfers between fixed points on opposite sides of the Earth. Finally, we present some novel methods for finding periodic orbits in circumstances in which traditional methods break down, based on considerations of the center manifold theorem.

Evolution of the L1 halo family in the radial solar sail circular restricted three-body problem

We present a detailed investigation of the dramatic changes that occur in the

Regular and irregular geodesics on spherical harmonic surfaces

\mathcal {L}_1

Even perturbations of the self-similar Vaidya space-time

L1 halo family when radiation pressure is introduced into the Sun–Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line. The problem is then parameterized by the sail lightness number, the ratio of solar radiation pressure acceleration to solar gravitational acceleration. Using boundary-value problem numerical continuation methods and the AUTO software package (Doedel et al. in Int J Bifurc Chaos 1:493–520, 1991) the families can be fully mapped out as the parameter

Bifurcations of the conjugate locus

\beta