  The dynamical behavior of spacecraft around asteroids is a key element in
design of such missions. An asteroid's irregular shape, non-spherical mass
distribution and its rotational sate make the dynamics of spacecraft quite
complex. This paper focuses on the gravity gradient torque of spacecraft around
non-spherical asteroids. The gravity field of the asteroid is approximated as a
2nd degree and order-gravity field with harmonic coefficients C20 and C22. By
introducing the spacecraft's higher-order inertia integrals, a full
fourth-order gravity gradient torque model of the spacecraft is established
through the gravitational potential derivatives. Our full fourth-order model is
more precise than previous fourth-order model due to the consideration of
higher-order inertia integrals of the spacecraft. Some interesting conclusions
about the gravity gradient torque model are reached. Then a numerical
simulation is carried out to verify our model. In the numerical simulation, a
special spacecraft consisted of 36 point masses connected by rigid massless
rods is considered. We assume that the asteroid is in a uniform rotation around
its maximum-moment principal axis, and the spacecraft is on the stationary
orbit in the equatorial plane. Simulation results show that the motion of
previous fourth-order model is quite different from the exact motion, while our
full fourth-order model fits the exact motion very well. And our model is
precise enough for practical applications.
