  The recently suggested SEE (Satellite Energy Exchange) method of measuring
the gravitational constant $G$, possible equivalence principle violation
(measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force
parameters $\alpha$ and $\lambda$ on board a drag-free Earth's satellite is
discussed and further developed. Various particle trajectories near a heavy
ball are numerically simulated. Some basic sources of error are analysed. The
$G$ measurement procedure is modelled by noise insertion to a ``true''
trajectory. It is concluded that the present knowledge of $G, \alpha$ (for
$\lambda \geq 1$ m) and $\eta$ can be improved by at least two orders of
magnitude.
