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?

 

[jbriggs444]

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.

 

[Dilema]

Thanks
jbriggs444
If you found a document that derived it please let me know.

 

[Vanadium 50]

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.

You could. But adding up the forces in tiny little steps looks a lot like integrating the forces in infinitesimal steps, and that's just energy.

I suspect that any derivation falls into this category - it's an obfuscated or at least decorated restatement of energy conservation.

 

[Herman Trivilino]

But adding up the forces in tiny little steps looks a lot like integrating the forces in infinitesimal steps, and that's just energy.

Right. It's the process used in calculus-based introductory physics textbooks to derive the expression for the electric potential energy. When one uses conservation of energy to find the escape velocity one is making use of the results derived from integrating the force.