  Several dynamical systems of interest in celestial mechanics can be written
in the form of a Newton equation with time-dependent damping, linear in the
velocities. For instance, the modified Kepler problem, the spin-orbit model and
the Lane-Emden equation all belong to such class. In this work we start an
investigation of these models from the point of view of contact geometry. In
particular we focus on the (contact) Hamiltonisation of these models and on the
construction of the corresponding geometric integrators.
