Gravitational Field

Gravitational Potential (V) The work done per unit mass in bringing a small test mass from infinity to a point in the gravitational field. It is a scalar quantity, always negative (since work is done by the field as the mass moves from infinity, meaning external work is negative). For a point mass M , V = -(GM)/(r) . The potential is zero at infinity and becomes more negative as you approach the mass. Example: Near Earth’s surface, V ≈ –62.5 MJ/kg (at surface), decreasing to –4.4 MJ/kg at geostationary orbit. Gravitational Potential Energy (U) The energy stored in a system of two (or more) masses due to their gravitational interaction. For two point masses m and M separated by distance r , U = -(GMm)/(r) . It is the work done to assemble the system from infinity. Negative U means the system is bound — you must add energy to separate them. Example: A satellite in orbit has negative total energy; to escape, you must supply enough kinetic energy to make total energy ≥ 0.