# Unusual escape velocity derivation

Dilema
Is it possible to derive escape velocity say using momentum and force balance considerations? or using angular momentum consideration?
Namely, any other approach then energy consideration that utilizes gravitation potential energy and kinetic energy?

Homework Helper
Summary: Does anyone knows other derivation then the usual energy conservation to the escape velocity: v=(2MG/r)^0.5?

Is it possible to derive escape velocity say using momentum and force balance considerations? or using angular momentum consideration?
Namely, any other approach then energy consideration that utilizes gravitation potential energy and kinetic energy?
One could, of course, attack the problem from first principles using forces and masses, determining a trajectory and evaluating the required initial velocity to reach a chosen distance using a particular launch angle. One could then take the limit as the target distance is allowed to increase without bound.

Similarly, one could exploit time reversal symmetry and use the same approach to determine the final velocity and impact angle for a drop from a large finite distance with a particular initial angular momentum and then take the limit as the initial distance is allowed to increase without bound.

But it is so much easier to use the fact the the gravitational field is conservative. It then follows immediately that the trajectory is irrelevant and that only the starting and ending points matter.

PeroK and anorlunda
Dilema
Thanks
jbriggs444
If you found a document that derived it please let me know.

Staff Emeritus