A Model Problem of Motion along the Handrail Constraint by a Solar Sail

Abstract

The paper considers the possibility of cargo relocation without fuel costs along a tether connecting two heavy space stations by a spacecraft with a controlled solar sail. The spacecraft’s relative motion dynamics is studied within the context of a model problem that assumes that the stations describe one heliocentric orbit, the solar sail is a perfect reflective flat panel, and the tether realizes an ideal unilateral handrail constraint that restricts the spacecraft relative motion to an ellipsoid. It is noted that, if the distance between stations is sufficiently small and the ratio of the sail area to the spacecraft mass is on the same order of magnitude as in already-implemented space missions, solar radiation is the main factor that influences the spacecraft’s motion in the orbital frame of reference. The problem of searching a set of pairs of points, between which relocation with a permanently oriented sail is possible, is solved for the pairs that belong to the intersection of the ellipsoid boundary and the plane of the stations’ orbit. The duration of the spacecraft relocation between the ellipsoid poles is estimated for the case of the sail oriented orthogonally to the solar rays. Also, the duration of the fastest relocation between poles is computed using special sail orientation control laws, including the case of zero initial and final velocities.