Hill's equation which describes approximately motions of interacting two bodies orbiting around the Sun is summarized, together with its properties. Hill's equation can be separated into equations of the relative and center of mass motions, and the center of mass motion can be integrated analytically. Further, it can be rewritten in a non-dimensional form scaled by the Hill radius and the heliocentric distance. These characteristics of Hill's equation reduce the degrees of freedom of particle motion and, hence, it is advantageous to use it in studies of gravitational scattering and collision between Keplerian particles, which will be described in later chapters.