For high-definition observation of GEO(geosynchronous orbit) spacecraft, the optical satellite approaches the GEO spacecraft with continuous low-thrust and flies around the GEO spacecraft without thrust. On the deviation of Clohessy-Wiltshire (CW) equations, CW equations are improved by accommodating the non-spherical perturbation, and the quadratic terms of the nonlinearity in the differential gravitational acceleration. The secular growth of the nonlinear deviation and the most perturbation deviation have been accommodated in the ICW (improved CW) equations. On trajectory planning, we calculate the initial phase angle interval of the fly-around trajectory to ensure that the optical satellite can take pictures of the GEO spacecraft with favorable observation angles throughout the entire fly-around mission. Simulations are conducted based on CW equations and ICW equations, respectively. The simulation based on the CW equations fails, but the simulation based on the ICW equations succeeds. The total thrust required is only 4.67 m/s, which is highly feasible in engineering.