The flight dynamics subsystem (FDS) of a geostationary satellite ground control system conducts estimates of the orbital states, keeping within its mission box, and calculating the satellite operational parameters to be uploaded. A new FDS has been designed and implemented by dividing it into core-and bus-dependent modules for a recent Korean geostationary satellite ground control system. The core modules include orbit determination and prediction, event prediction, and station-keeping and relocation (SKR) planning; whereas the bus-dependent modules include fuel accounting, thruster modeling and maneuver reconstructions of SKR, and calculate all of the bus-dependent parameters. In particular, separate designs based on the components of the SKR planning and maneuver reconstruction using thruster modeling allow the system to be reusable and replaceable. We also designed and implemented a conjunction analysis tool and collocation control and monitoring units for multiple-satellite control. A FDS database has been developed and is managed using SQLite, which is freely distributed. The FDS is easy to develop and operate thanks to a novel separation concept introduced for the core-platform and spacecraft bus-dependent modules. It is the same concept used for operation and the graphical user interfaces (GUIs) applicable to the FDS. All of the FDS modules for new geostationary satellites have been validated through function and performance testing, and have proven to work successfully after the launch of satellites.