  The trajectory of a spherical object which falls freely in a gravitational
field is fixed by its initial position and velocity. However, an object which
can control its shape can also control its motion: Except where forbidden by
symmetries and their associated conservation laws, a shape-changing (but
rocket-free) spacecraft can have complete control over its trajectory. We
discuss a general formalism which allows rocket-free maneuvers to be understood
without constructing detailed interior models. A spacecraft's interior is
abstracted to the specification of a quadrupole moment, and in some cases, it
is only a single eigenvalue of that moment which is relevant. For orbits around
a spherically-symmetric mass, we show that appropriately varying the relevant
eigenvalue allows the energy and eccentricity of an orbit to be increased or
decreased and its apsides to be rotated arbitrarily. Strategies are identified
which optimize these maneuvers. In other contexts, we show that extended-body
effects can be used to stabilize orbits which would otherwise be unstable.

General Relativity and Quantum Cosmology;Space Physics