### Spacecraft Dynamics near an Asteroid Pair

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 study depending 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 the spacecraft is observing
the asteroid pair.

PAPERS

**Binary Asteroids Observation Orbits from a Global Dynamical Picture**, submitted to *SIAM Journal on Applied Dynamical Systems*. (Gabern, F., W.S. Koon, J.E. Marsden, and D.J. Scheeres [2005], pdf)

**Parking a Spacecraft near an Asteroid Pair**, *Journal of Guidance, Control and Dynamics*, Vol. 29, N. 3, pp. 544-553. (Gabern, F., W.S. Koon, and J.E. Marsden [2006], pdf)

**Spacecraft Dynamics near a Binary Asteroid**, *Dynamical Systems and Differential Equations (edited by Hu, Lu and Xie)* [2005], pages 297-306. (Gabern, F., W.S. Koon, and J.E. Marsden, pdf)

**Geometric Mechanics and the Dynamics of Asteroid Pairs**, *New Trends in Astrodynamics and Applications*, University of Maryland, College Park. (Koon, W.S., J.E. Marsden, S.D. Ross, M.W. Lo, and D.J. Scheeres [2003], pdf)