Time-optimal solar sail heteroclinic-like connections for an Earth-Mars cycler

Abstract

This paper investigates solar sail Earth-Mars cyclers, in particular cyclers between libration point orbits at the Earth-Moon L 2 point and the Sun-Mars L 1 point. In order to facilitate cyclers in as few Earth-Mars synodic periods as possible, the overall objective is to minimize the time of flight. These time-optimal cyclers are obtained by using a direct pseudospectral method and exploiting techniques from dynamical systems theory to obtain an initial guess. In particular, heteroclinic connections between the unstable and stable manifolds of the target libration point orbits at the Earth-Moon L 2 point and the Sun-Mars L 1 point are sought for. While such connections do not exist in the ballistic case, they can be achieved by complementing the dynamics with a solar sail and assuming a constant attitude of the sail with respect to the direction of sunlight. These trajectories are sub-optimal due to the assumed constant sail attitude as well as minor discontinuities in position and velocity at the linkage of the manifolds, which are overcome by transferring the initial guess to the direct pseudospectral optimal control solver. For near-to mid-term sails, results show time-optimal round-trip trajectories that span three synodic Earth-Mars periods, with a few months to one year stay times at the libration point orbits, depending on the time of departure within a five-month window. Through the propellant-less nature of solar sailing, these Earth-Mars cyclers can, in theory, be maintained indefinitely.

Homo- and Heteroclinic Connections in the Planar Solar-Sail Earth-Moon Three-Body Problem

“…Trajectories along these manifolds can be obtained by propagating the dynamics in Equation (1) from a state-vector along the stable and unstable eigenvectors of the linearized system around the periodic orbit, i.e., the reference trajectory, r 0 . Replacing r → r 0 + δr in Equation 1gives the following linearized system δẋ = Aδx (6) and…”

“…In recent years, the L 1 and L 2 libration points of the Earth-Moon system have drawn renewed interest as they hold potential to support future human space exploration activities. Such support may come in the form of landing missions [1,2], lunar farside communication capabilities [3,4], or as a gateway to more distant interplanetary destinations [1,5,6]. The natural motion around the libration points has been studied in great detail [7][8][9] and several families of (quasi-)periodic orbits around the libration points have been identified, e.g., Lissajous [10], Lyapunov [11], and halo [12] orbits, with more families in, for example, Kazantzis [13,14].…”

Photon-Sail Equilibria in the Alpha Centauri System

“…Using the obtained trajectory as an initial guess for more advanced numerical methods, such as multiple shooting differential correction, or even optimization methods, will allow more frequent and smoother sail attitude changes along the trajectory. Such an approach has already been demonstrated to be successful for finding photon-sail heteroclinic-like connections in and between a range of Sun-planet systems [15][16][17] for linkage errors of similar magnitude and may therefore also allow finding feasible and potentially time-optimal transfers in the α-Cen AB system.…”

“…As a final novel contribution, this Note investigates heteroclinic-like connections between the newly found equilibria. Again, while photon-sail heteroclinic-like connections have been investigated within our own single-star Solar System [15][16][17], the search for such transfers under the effect of two radiative stars is new and allows further insights in the dynamics and maneuverability of a photon-sail in a two-radiative ER3BP such as that of the Alpha Centauri system.…”