Solar Sail Capabilities to Reach Elliptic Rectilinear Orbits

An elliptic rectilinear orbit (ERO) is a particular conic orbit in which the semimajor axis takes a finite value and the eccentricity is unity. From a geometrical point of view an ERO is a line segment connecting both orbital foci: one endpoint of the segment coincides with the primary focus (the sun in a heliocentric system), while the other endpoint is the orbit apocenter. A spacecraft (or a celestial body) that tracks a heliocentric ERO experiences a rectilinear motion toward the sun with a purely radial velocity, that is, directed along the spacecraft-sun direction. The velocity magnitude is zero in correspondence of the orbit apocenter and takes its maximum value at the primary focus.