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Binary Asteroid Observation Orbits from a Global Dynamical Perspective

Gabern, F. and Koon, W. S. and Marsden, J. E. and Scheeres, D. J. (2006) Binary Asteroid Observation Orbits from a Global Dynamical Perspective. SIAM Journal on Applied Dynamical Systems, 5 (2). pp. 252-279. ISSN 1536-0040. doi:10.1137/050641843.

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We study spacecraft motion near a binary asteroid by means of theoretical and computational tools from geometric mechanics and dynamical systems. We model the system assuming that one of the asteroids is a rigid body (ellipsoid) and the other a sphere. In particular, we are interested in finding periodic and quasi-periodic orbits for the spacecraft near the asteroid pair that are suitable for observations and measurements. First, using reduction theory, we study the full two body problem (gravitational interaction between the ellipsoid and the sphere) and use the energy-momentum method to prove nonlinear stability of certain relative equilibria. This study allows us to construct the restricted full three-body problem (RF3BP) for the spacecraft motion around the binary, assuming that the asteroid pair is in relative equilibrium. Then, we compute the modified Lagrangian fixed points and study their spectral stability. The fixed points of the restricted three-body problem are modified in the RF3BP because one of the primaries is a rigid body and not a point mass. A systematic studydepending on the parameters of the problem is performed in an effort to understand the rigid body effects on the Lagrangian stability regions. Finally, using frequency analysis, we study the global dynamics near these modified Lagrangian points. From this global picture, we are able to identify (almost-) invariant tori in the stability region near the modified Lagrangian points. Quasi-periodic trajectories on these invariant tori are potentially convenient places to park the spacecraft while it is observing the asteroid pair.

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Additional Information:© 2006 SIAM Received by the editors October 4, 2005; accepted for publication (in revised form) by T. Kaper February 14, 2006; published electronically June 2, 2006. This work was partly supported by the California Institute of Technology President’s Fund, NSF-ITR grant ACI-0204932, NSF grant DMS-0505711, and by ICB, the Institute for Collaborative Biotechnologies, through ARO grant DAAD19-03-D-0004. This author [D.J.S.] acknowledges support from the Jet Propulsion Laboratory/California Institute of Technology through a grant from the Director’s Research Discretionary Fund. The authors thank J. M. Mondelo for providing them with a program for frequency analysis.
Subject Keywords:asteroid pairs, spacecraft dynamics, stability, frequency analysis, invariant tori, quasi-periodic motion
Issue or Number:2
Record Number:CaltechAUTHORS:GABsiamjads06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4129
Deposited By: Archive Administrator
Deposited On:28 Jul 2006
Last Modified:08 Nov 2021 20:15

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