The velocity v required for a projectile to escape from a massive body to a point at infinity (which it will reach after an infinite amount of time with speed zero). Let the projectile have mass m, and the central body have mass M. Then equating the initial kinetic energy of the projectile with the potential energy relative to mass M at a distance r from the center of M gives

(1)

where G is the gravitational constant. Solving for v gives

(2)

This is the escape velocity,

(3)

which can be seen is also a factor of larger than the orbital speed of a body in a circular orbit at orbital radius a.

Let . If R < 1, the body does not reach , and if R = 1, then the body reaches with speed 0.

c3, Jeans Escape, Vis-Viva Equation