On a Sailed Spacecraft Motion along a Handrail Fixed to Two Heliocentric Space Stations

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.