Solar sail Lyapunov and Halo orbits in the Earth–Moon three-body problem

Abstract

Solar sailing has been proposed for a range of novel space applications, including hovering above the ecliptic for high-latitude observations of the Earth and monitoring the Sun from a sub-L 1 position for space weather forecasting. These applications, and many others, are all defined in the Sun-Earth threebody problem, while little research has been conducted to investigate the potential of solar sailing in the Earth-Moon three-body problem. This paper therefore aims to find solar sail periodic orbits in the Earth-Moon three-body problem, in particular Lagrange-point orbits. By introducing a solar sail acceleration to the Earth-Moon three-body problem, the system becomes non-autonomous and constraints on the orbital period need to be imposed. In this paper, the problem is solved as a twopoint boundary value problem together with a continuation approach: starting from a natural Lagrange-point orbit, the solar sail acceleration is gradually increased and the result for the previous sail performance is used as an initial guess for a slightly better sail performance. Three in-plane steering laws are considered for the sail, two where the attitude of the sail is fixed in the synodic reference frame (perpendicular to the Earth-Moon line) and one where the sail always faces the Sun.The results of the paper include novel families of solar sail Lyapunov and Halo orbits around the Earth-Moon L 1 and L 2 Lagrange points, respectively. These orbits are double-revolution orbits that wind around or are off-set with respect to the natural Lagrange-point orbit. Finally, the effect of an out-of-plane solar sail acceleration component and that of the Sun-sail configuration is investigated, giving rise to additional families of solar sail periodic orbits in the Earth-Moon three-body problem.

Exploring the Heliogyro’s Orbital Control Capabilities for Solar Sail Halo Orbits

“…Many works in the literature (e.g., References [22][23][24][26][27][28]) describe methods to find solar sail periodic (halo) orbits under the dynamics described in Eq. (11) or similar systems.…”

Novel solar sail mission concepts for high-latitude Earth and lunar observation

“…Besides adding an additional family of solar sail orbits to previous work, see Reference [13,14], this paper also investigates, for the first time, the effect of higher-fidelity dynamics on the existence and properties of the solar sail periodic orbits presented. While previous work assumed that the ecliptic and Earth-Moon planes coincide and neglected the lunar eccentricity, this paper accounts for these effects, providing realistic solar sail trajectories by expanding the differential correction technique to a multiple shooting differential correction method.…”

“…These orbits can be found through the use of differential correction techniques: by perturbing classical libration point orbits such as Lyapunov, halo, vertical Lyapunov and distant retrograde orbits with a solar sail induced acceleration, entirely new families of orbits result in the Earth-Moon system parametrised by the sail's acceleration [13,14]. Different types of families can be created depending on the steering law assumed for the solar sail.…”

Extension of Earth-Moon libration point orbits with solar sail propulsion

“…The results in the linearised system have been transferred to the full non-linear dynamical system (Wawrzyniak and Howell 2011a), but the results presented are limited to one specific steering law and only show one family of orbits at the Earth-Moon L 2 point. Initial results on more extensive families of solar sail periodic orbits in the Earth-Moon system do exist (Heiligers et al 2015), but have been found by solving a two-point boundary value problem, while this paper develops a faster and more accurate differential correction scheme. Furthermore, this paper significantly extends the families found in (Heiligers et al 2015) to Lyapunov, halo, and vertical Lyapunov orbits around both the L 1 and L 2 points as well as Earth-centred and distant retrograde orbits.…”

“…Initial results on more extensive families of solar sail periodic orbits in the Earth-Moon system do exist (Heiligers et al 2015), but have been found by solving a two-point boundary value problem, while this paper develops a faster and more accurate differential correction scheme. Furthermore, this paper significantly extends the families found in (Heiligers et al 2015) to Lyapunov, halo, and vertical Lyapunov orbits around both the L 1 and L 2 points as well as Earth-centred and distant retrograde orbits. Finally, this paper investigates for the first time the stability properties of these orbits in order to assess the effect of the solar sail on the orbit stability compared to the classical libration point orbits and the potential need for active orbital control.…”