Abstract: When an objective spacecraft （OS） moves along a near circular orbit in unpowered flight, the relative motion of a controlled spacecraft （CS） relatively to the OS is described approximately by the Hill equations on condition that the CS is near to the OS. The Hill equations are solved on the assumption that the thrust acceleration of the CS is the linear function of time. The equation of specific kinetic energy （ESKE） for the relative motion of the two close spacecrafts is deduced from the Hill equations. The applications of ESKE to orbit meet and orbit rendezvous are discussed.