  We derive the equations of celestial mechanics governing the variations of
the orbital elements under a stochastic perturbation generalizing the classical
Gauss equations. Explicit formulas are given for the semi-major axis, the
eccentricity, the inclination, the longitude of the ascending node, the
pericenter angle and the mean anomaly which are express in term of the angular
momentum vector $\textbf{H}$ per unit of mass and the energy $E$ per unit of
mass. Together, these formulas are called the \emph{stochastic Gauss equations}
and they are illustrated numerically on an example from satellite dynamics.
