Solar Sail Capabilities to Reach Elliptic Rectilinear Orbits

Abstract

A N ELLIPTIC rectilinear orbit (ERO) is a particular conic orbit in which the semimajor axis takes a finite value and the eccentricity is unity [1]. Froma geometrical point of view anERO 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 sunwith 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. Apart from the theoretical mathematical interest of such orbits, the practical importance of a rectilinear trajectory toward the sun involves different possible scientific missions, such as those concerning the test of the equivalence principle, the analysis of the interstellar dust, or the study of the radial variation of the solar wind. In addition, an ERO could be useful for a detailed analysis of the sun’s gravitational harmonics [2,3]. Themain obstacle against the use of anERO for scientificmissions is mainly due to the substantial amount of propellant required to reach these orbits. To get a rough estimate, consider the minimum V necessary to transfer a spacecraft from a heliocentric circular orbit of radius r0 to a coplanar ERO with an aphelion radius ra > r0. Assuming a bi-impulsive maneuver and a Hohmann-like elliptic transfer orbit with semimajor axis r0 ra =2, the total velocity variation necessary to complete the transfer is