  Free-fall is only approximately universal in general relativity. Different
extended bodies can fall in different ways, depending on their internal
dynamics. Nevertheless, certain aspects of their motion are universal. This
paper examines the universal constraints on extended-body motion in vacuum type
D spacetimes. Working in the quadrupole approximation, we show that in addition
to the (previously-known) constraints imposed by Killing vectors, two
components of the gravitational torque must vanish. Furthermore, of the ten
components of a body's quadrupole moment, four are found to be irrelevant, two
can affect only the force, and the remaining four can affect both forces and
torques. As an application, we consider the capabilities of a hypothetical
spacecraft which controls its motion by controlling its internal structure. In
the Schwarzschild spacetime, such a spacecraft can control its mass, and in
doing so, it can stabilize unstable orbits, escape from bound orbits, and more
-- all without a rocket.
