Resonant Orbits Characteristics of Solar Sails Near the L2 Point in the Earth–Moon System

Аuthors

Yu W. ^*, Starinova O. L.^**

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: yussau@foxmail.com
**e-mail: solleo@mail.ru

Abstract

As part of future lunar exploration and development projects, relay satellites for communication between the Earth and the Moon, especially the far side and polar regions of the Moon, where permanent bases are planned to be built, are attracting significant interest. This work is devoted to studying the characteristics of resonant orbits of solar sails near the L2 point in the Earth-Moon system, which are considered as potential trajectories for Earth-Moon relay satellites. A method is formulated in this article to ascertain resonant orbits near the L2 point, employing the multiple shooting method to solve a two-point boundary value problem with the goal of closing the spacecraft's trajectory to form a periodic orbit. Those resonant orbits formed based on Lyapunov orbits as initial approximations in two-point boundary value problems are called Lyapunov conformal orbits, and orbits formed based on halo orbits are called halo conformal orbits. An exploration is also executed on how resonant orbits vary concerning solar sail control variables, encompassing the initial position of the Sun, the magnitude of the nominal acceleration from light pressure and the installation angles of the solar sails. In result, such conclusions were obtained: 1. the influence of the initial position of the Sun divides the resonant orbits into different groups with different configurations; 2. the influence of the magnitude of the nominal acceleration determines the displacement of resonant orbits relative to natural periodic orbits, and Lyapunov conformal orbits have different changing trends of displacement compared with halo conformal orbits; 3. the influence of the installation angles of the solar sails mainly determines the displacement of the resonant orbits relative to natural periodic orbits in the out-of-plane direction, and for all orbits the maximum displacements obtain extreme values at ±35,26°.
 As a result of the research, the types and number of periodic orbits for placing Earth-Moon relay satellites were expanded, and dependencies for changes in resonant orbits were obtained. It should be noted that, in contrast to the orbits of traditional spacecrafts, the positions of spacecrafts with solar sails in resonant orbits are time dependent. Therefore, orbital phasing turns out to be an important component in the mission of insertion into a resonant orbit and requires additional research.

Keywords:

resonant orbit, solar sail, L2 libration point, Earth-Moon system, multiple shooting method, initial position of the Sun, nominal acceleration magnitude, solar sail installation angles

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