Influence of the Earth’s Dominant Oblateness Parameter on the Low Formation Orbits of Micro-Satellites

Abstract

The objective of the present work is to investigate the effect of the Earth’s oblateness parameters, particularly J₂, on the formation flight of micro satellites in low circular orbits. For this purpose, the Clohessy-Wiltshire equations, which have been accordingly  modified, will be reviewed to arrive at a convenient formulation as a set of linearized differential equations of motion to include the J₂ effects in the LVLH frame of reference. Comparison will then be made between the orbit of twin-satellite formation flying with respect to that predicted by the Hill-Clohessy-Wiltshire equation. Results obtained compare well with those in the literature and can be utilized for further development, parametric studies and mission design.