  We analyze the trajectories of three geostationary satellites forming the
GEOstationary GRAvitational Wave Interferometer (GEOGRAWI)~\cite{tinto}, a
space-based laser interferometer mission aiming to detect and study
gravitational radiation in the ($10^{-4} - 10$) Hz band.
  The combined effects of the gravity fields of the Earth, the Sun and the Moon
make the three satellites deviate from their nominally stationary, equatorial
and equilateral configuration. Since changes in the satellites relative
distances and orientations could negatively affect the precision of the laser
heterodyne measurements, we have derived the time-dependence of the
inter-satellite distances and velocities, the variations of the polar angles
made by the constellation's three arms with respect to a chosen reference
frame, and the time changes of the triangle's enclosed angles. We find that,
during the time between two consecutive station-keeping maneuvers (about two
weeks), the relative variations of the inter-satellite distances do not exceed
a value of $0.05$ percent, while the relative velocities between pairs of
satellites remain smaller than about $0.7 \ {\rm m/s}$. In addition, we find
the angles made by the arms of the triangle with the equatorial plane to be
periodic functions of time whose amplitudes grow linearly with time; the
maximum variations experienced by these angles as well as by those within the
triangle remain smaller than $3$ arc-minutes, while the East-West angular
variations of the three arms remain smaller than about $15$ arc-minutes during
the two-weeks period. The relatively small variations of these orbit parameters
result into a set of system functional and performance requirements that are
less stringent than those characterizing an interplanetary mission.
