Родников Александр Владимирович

The possibility of keeping a spacecraft with a solar sail near an unstable triangular libration
point of a minor planet or a binary asteroid is studied under the assumption that only the
gravitation and the solar radiation influence the spacecraft motion. The case where the solar
sail orientation remains unchanged with respect to the frame of reference of the heliocentric
orbit of the asteroid mass center is considered. This means that the angle between the solar sail
normal and ecliptic, as well as the angle between this normal and the solar rays at the current
point, does not change during the motion. The spacecraft equations of motion are deduced under
assumptions of V.V. Beletsky’s generalized restricted circular problem of three bodies, but taking
into account the Sun radiation. The existence of a manifold of initial conditions for which it is
possible to choose the normal direction that guarantees the spacecraft bounded motion near the
libration point is established. Moreover, the dimension of this manifold coincides with that of
the phase space of the problem at which the libration point belongs to the manifold boundary. In
addition, some proposals for stabilization of the spacecraft motions are formulated for trajectories
beginning in the manifold.

Motion of a particle modeling a spacecraft with a solar sail along a handrail joining two heliocentric space stations is considered under the assumption that the sail is a perfect reflecting plane that can be located at any angle with respect to the direction of solar rays, the particle does not leave the plane of the orbit of the stations, the handrail is a tether that realizes an ideal unilateral constraint whose boundary is some ellipse, and the particle motion is sufficiently fast with respect to the orbital motion of the stations to neglect noninertiality of the orbital frame of reference. The equations of particle motion are written in dimensionless form without parameters, and the existence of an energy integral for the case of the sail orientation depending only on the spacecraft location is established. This integral is used for complete integration of the equations of motion for the particle relocations along the constraint boundary. The optimal length of the tether for the fastest relocation of a particle between the most remote points of the constraint boundary is computed for the case of the sail being orthogonal to the solar rays throughout the motion. Such a relocation time is computed in dimensionless form and for some real and hypothetical situations. A set of pairs of points in the constraint boundary between which relocation along the constraint boundary with zero initial and final velocities and with the invariably oriented sail is possible is constructed depending on the eccentricity of the ellipse. The result is presented as several plots that illustrate the evolution of the pairs’ regions as the eccentricity of the ellipse changes.