Solar sail formation flying around displaced solar orbits

R ECENTLY, attention has been focused on solar sail missions, such as the new artificial Lagrange points created by solar sails to be used to provide early warning of solar plasma storms, before they reach Earth [1,2]. There are several prior references with regard to such orbits in the literature. As early as 1929, Oberth mentioned in his study that solar radiation pressure would displace a reflector in an Earth polar orbit in the anti-sun direction, so that the orbit plane did not contain the center-of-mass of the Earth [3]. Later, in 1977, Austin et al. [4] noted that propulsive thrust can be used to displace the orbit of an artificial body, but only small displacements were considered for spacecraft proximity operations, and no analysis of the problem was provided. Similarly, Nock suggested a displaced orbit above Saturn’s rings for in situ observation, however, again no analysis was given [3]. In 1981, Forward [5] considered a displaced solar sail north or south of the geostationary ring. However, because he did not use an active control, subsequent analysis has criticized thiswork and claimed that such orbits were impossible. More recently, McInnes and Simmons have done work in which large families of displaced orbits were found by considering the dynamics of a solar sail in a rotating frame [6], and the dynamics, stability, and control of different families of displaced orbits were investigated in detail [7,8]. Based on McInnes’ and Simmons’ work [6], Molostov and Shvartsburg considered a more realistic solar sail model with nonperfect reflectivity and discussed the effect of finite absorption of the sail on the displaced orbits [9,10]. However, studies of the relative motion of solar sails are rare in the literature. The original idea of formation flying around a displaced orbit considered in this note comes from the concept of combining a displaced orbit with formation flying to achieve greater resolution than a single sail for science missions. This note outlines the characteristics of the relative motion around a displaced solar orbit and proposes some possible control strategies. Because the relative distance between the sails is very small compared with the distance from the sun to the sails, the relative equation of motion is linearized in the vicinity of a displaced solar orbit. Based on the linearized equation, two types of formations, seminatural and controlled formations, are discussed. The seminatural formations are performed with only sail attitude variations, but configurations of the relative orbits strongly depend on the orbit of the leader sail. Therefore, more complex controllers are adopted to build more sophisticated formations to meet special demands on the relative orbit configurations.