Gravitational Potential Energy (Orbital)

Gravitational potential energy is negative by convention: the zero is set at infinite separation, and every real pair of masses sits below it, in an energy "well" of depth GMm/r. A 1 000 kg satellite at the ISS's orbital radius, r = 6.79 × 10⁶ m, has U = −6.674 × 10⁻¹¹ × 5.97 × 10²⁴ × 1 000 / 6.79 × 10⁶ ≈ −5.87 × 10¹⁰ J — about 59 GJ that a launch vehicle must partly repay to lift it there from the surface, plus the kinetic energy of orbit.

The minus sign carries real physics. A bound orbit has total energy E = U/2 (the virial theorem's ½ shows up here: kinetic energy equals half the well depth), and escaping requires pumping E up to zero — which is exactly where the escape-velocity formula comes from. It also produces gravity's strangest habit: drag a satellite down and it speeds up, because falling deeper into the well converts potential energy into more kinetic energy than the drag removes.