New Periodic Orbits in the Solar Sail Three-Body Problem

Abstract

In this paper we consider periodic orbits of a solar sail in the Earth-Sun restricted three-body problem. In particular, we consider orbits which are high above the ecliptic plane, in contrast to the classical Halo orbits about the collinear equilibria. We begin with the Circular Restricted Three-Body Problem (CRTBP) where periodic orbits about equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the Elliptic Restricted ThreeBody Problem (ERTBP). A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e = 0 and continuing to the required eccentricity of e = 0.0167. The stability of these periodic orbits is investigated.

Solar Sail Formation Flying for Deep-Space Remote Sensing

“…This paper extends the work of Biggs et al [10], who identify a 1-year periodic orbit high above the ecliptic plane in the solar sail ERTBP. Biggs et al [10] used the method of Lindstedt-Poincaré to obtain high-order approximations of periodic orbits above the ecliptic in the solar sail circular restricted three-body problem [3].…”

“…As the value of the lightness number will determine the distance of the Earth from the platform, it will have a direct impact on mission costs. Biggs et al [10] and Waters and McInnes [3] give a plot of the artificial equilibria above the ecliptic for different values of for the case of the solar sail circular (e 0) restricted three-body problem. These equilibrium points are then used as a starting point to generate periodic orbits in the solar sail restricted three-body problem.…”

“…The continuation algorithm is based on a monodromy variant of Newton's method [11]. The initial orbit that will serve as a starter in the numerical continuation is given in the solar sail ERTBP [10]. In this section, we find 1-year periodic orbits above the ecliptic in the solar sail ERTBP described by the nonlinear system _ Xt FXt; t, where Xt x; y; z; x 0 ; y 0 ; z 0 .…”

“…Biggs et al [10] used the method of Lindstedt-Poincaré to obtain high-order approximations of periodic orbits above the ecliptic in the solar sail circular restricted three-body problem [3]. Following this, the high-order approximations were used as an initial guess in a differential corrector to obtain closed orbits in the full nonlinear model.…”

Families of halo orbits in the elliptic restricted three-body problem for a solar sail with reflectivity control devices

“…Gong and Li (2015b) generated the out-of-plane periodic orbits in the SSER3BP by adjusting the sail angles together with the out-of-plane position to satisfy the equilibrium equations. Biggs et al (2008 and Farrés and Jorba (2011) investigated one-year periodic orbits in the SSER3BP. Biggs et al (2008 computed a one-year out-of-plane orbit in the solar sail CR3BP (SSCR3BP) and used this as a seed to numerically continue periodic orbits in the SSER3BP.…”