On Utilization of Solar Sails in Triangular Libration Point Missions in the Earth-Moon System

Abstract

In the real solar system, due to various perturbations, the triangular libration points of the earth-moon system are unstable. However, there are quasi-periodic orbits around them. These orbits show mild instability. Due to the instability, orbit control is necessary for the spacecrafts around these points. In the paper, solar sails were taken to fulfill the control. Numerical simulations were made in the earth-moon system. The results showed that taking the surface of the solar sail as the control parameter can achieve better results. Triangular Libration points in the earth-moon system have fixed configurations with the earth and the moon. This geometrical property is ideal for some space missions. For example, relay stations can be put around them. Spacecrafts can also be sent to these points for deep space observations. Along with the observations on earth, better observation data can be obtained. Besides this, these points are ideal potential candidates for space VLBI observations. In the restricted three-body problem of the earth-moon system, the mass ratio μ is smaller than Routh’s critical value μ1=0.03852…. They are linearly stable in the restricted three-body problem 1) . However, in the real solar system, various perturbations (mainly the gravitational perturbations from the sun) change their dynamical properties and these points are no longer stable anymore. Nevertheless, quasi-periodic orbits staying around them can be found. These orbits show mild instability. Due to their instability, orbit control is necessary for the spacecrafts moving on these orbits. Solar sails can produce long-lasting thrust and do not require any fuels. It’s an ideal choice for space missions. They were taken to fulfill the orbit control in this paper. The magnitude and direction of the thrust produced by the solar sail are coupled, and the force is always directed away from the sun. This is one shortcoming of the solar sails. Due to this property, instead of the tight control strategy, we took a loose one. This strategy needs a pre-determined nominal orbit. A quasi-periodic orbit around the triangular libration points was chosen as the nominal orbit. Two sets of different control variables were used. One set is the surface of the solar sail, and the other one is the normal direction angles of the solar sail. Numerical simulations were done in the earth-moon system. The results showed that taking the surface of the solar sail as the control variable is better. During the lifetime of the spacecraft, it may be shadowed from the sun by the earth or the moon. The solar sail is of no use when the spacecraft is in the shadow. In order to avoid the shadows, the initial epoch of the nominal orbit is carefully chosen. Since the inclination angle between the moon’s and the sun’s orbit planes is small, the z amplitude motion of the nominal orbit is chosen to be large to avoid the shadows too. For a short time mission, these steps can avoid the shadows. For a long time mission, the spacecraft will encounter the shadows anyway. At the end of the paper, a discussion of this case was made. For the shadows in the paper, cylindrical model was considered.