The energy an object possesses due to its position in a gravitational field; it's negative, with zero defined at infinity.

The minimum speed an object needs to escape the gravitational pull of a central object.

The sum of kinetic and gravitational potential energy of a satellite in orbit.

The point in an orbit closest to the central object.

The point in an orbit farthest from the central object.

Circular: Constant kinetic and potential energy, constant total mechanical energy. Elliptical: Fluctuating kinetic and potential energy, constant total mechanical energy.

Circular: Constant speed. Elliptical: Speed varies; highest at periapsis, lowest at apoapsis.

1. Start with the total mechanical energy equation: $E = \frac{1}{2}mv^2 - \frac{GMm}{r}$. 2. Set the total energy to zero for escape: $0 = \frac{1}{2}mv_{esc}^2 - \frac{GMm}{r}$. 3. Solve for $v_{esc}$: $v_{esc} = \sqrt{\frac{2GM}{r}}$.