It's another energy balance equation, though: energy to start with is the same as energy that you end with. Suppose that we start a distance r0 from the Earth and end a distance r1 from the Moon, then the energy balance gives:
1 v02 - G M / r0 - G m / (D - r0) = 1 v12 - G M / (D - r1) - G m / r1
...where m is the moon's mass.
One simple limit takes D ? ? and 1 v02 ? G M / r0 (the escape velocity equation), to yield:
1 v12 ? G M / r1
v1 ? ?( 2 G M / r1 ) = 2377 m/s.
