Solar Sail Orbit Operations at Asteroids: Exploring the Coupled Effect of an Imperfectly Reflecting Sail and a Nonspherical Asteroid

This paper continues the work of previous studies which examined solar sail dynamics about an asteroid. In the current study the e ect of an imperfectly re ecting sail on the spacecraft dynamics is evaluated and the e ect of a non-spherical asteroid is explored. The e ect of the imperfect sail is seen to cause a diminished solar radiation pressure force along the sun line and modi es the possible hovering locations. The e ect of a non-spherical asteroid is modeled by using the J2 gravity eld contribution. We nd explicit predictions for the coupling between the (assumed dominant) solar radiation pressure and the gravity eld perturbation. Although the special class of stable orbits for solar sails are generally stable under the J2 perturbation, we nd certain parameter combinations that may lead to instabilities in the sail orbit. The analytical work is veri ed by numerical computations. Introduction The natural appeal of solar sailing coupled with the development of microtechnologies and new materials has recently caused increased interest in this eld. At the same time, we are just beginning to study asteroids in situ. Because solar sail spacecraft have an inexhaustable fuel supply from sunlight, they are capable of performing long term, multiple objective missions to asteroids, signi cantly decreasing the time between missions. They are also Copyright c 2002 The American Institute of Aeronautics and Astronautics Inc. All rights reserved. AIAA Paper 20024991 yResearch Associate, California Space Institute, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA zAssistant Professor, Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI xAssociate Research Physicist, California Space Institute, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA capable of orbiting asteroids or hovering over the surface for extended periods of time which allows surface mapping or sample returns. In our rst paper1, we examined the feasibility of both asteroid orbits and equilibrium points, making many assumptions on both the spacecraft and asteroid, i.e., that the spacecraft is perfectly re ecting and planar and that the asteroid is a point mass in a circular orbit about the sun. In our current analysis we relax some of these assumptions in an e ort to move toward a more realistic model of sail motion about an asteroid. We change the sail from being perfectly re ecting to imperfectly re ecting. Ideally, all photons incident on the sail will be re ected. In reality, however, some of the photons will be absorbed into the sail material. The eÆciency of the sail will decrease depending on the materials used. For the sake of this paper, we are assuming 85% re ectivity, which is a conservative estimate. Materials are available now which can achieve about 90% re ectivity.2 We also generalize the asteroid gravity eld from a point mass to an oblate spheroid with its rotation axis tilted away from the asteroid orbit angular momentum. The asteroid spin axis is xed in inertial space. Since the asteroid spin pole is about the symmetry axis, we do not consider the asteroid spin rate. Though we add in perturbations due to oblateness, we still neglect perturbations due to asteroid ellipticity. We make this assumption since the largest perturbation comes from the J2 e ect and because the sail will probably be placed in an orbit which minimizes the e ect of the asteroid ellipticity in general. Imperfectly re ecting sail model When taking an imperfectly re ecting solar sail into consideration, the solar radiation pressure (SRP) acceleration vector is no longer strictly nor1 AIAA/AAS Astrodynamics Specialist Conference and Exhibit 5-8 August 2002, Monterey, California AIAA 2002-4991 Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. mal to the sail. The equation for SRP for a perfectly re ecting sail is a = ap(l n)2n. For an imperfectly re ecting sail we must include a component of force in the transverse direction to the sail normal due to absorption of photons: