  Today, the motion of spacecraft is still described by the classical Newtonian
equations of motion plus some relativistic corrections. This approach might
become cumbersome due to the increasing precision required. We use the
Relativistic Motion Integrator (RMI) approach to numerically integrate the
native relativistic equations of motion for a spacecraft. The principle of RMI
is presented. We compare the results obtained with the RMI method with those
from the usual Newton plus correction approach for the orbit of the BepiColombo
(around Mercury) and Mars-NEXT (around Mars) orbiters. Finally, we present a
numerical study of RMI and we show that the RMI approach is relevant to study
the orbit of spacecraft.
