Detailed observations of geosynchronous satellites from earth are very limited. To better inspect these high altitude satellites, the use of small, refuelable satellites is proposed. The small satellites are stationed on a carrier platform in an orbit near the population of geosynchronous satellites. A carrier platform equipped with deployable, refuelable SmallSats is a viable option to inspect geosynchronous satellites. The propellant requirement to transfer to a targeted geosynchronous satellite, perform a proximity inspection mission, and transfer back to the carrier platform in a nearby orbit is determined. Convex optimization and traditional optimization techniques are explored, determining minimum propellant trajectories. Propellant is measured by the total required change in velocity, delta-v. The trajectories were modeled in a relative reference frame using the Clohessy-Wiltshire equations. Mass estimations for the carrier platform and the SmallSat were determined by using the rocket equation. The mass estimates were compared to the mass of a single, non-refuelable satellite performing the same geosynchronous satellite inspection missions. From the minimum delta-v trajectories and the mass analysis, it is determined that using refuelable SmallSats and a carrier platform in a nearby orbit can be more effcient than using a single non-refuelable satellite to perform multiple geosynchronous satellite inspections.