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Escape Velocity: Formula for GPE

In the derivation of escape velocity you need to equate the KE of the body trying to escape and the GPE. In this case why does the GPE go as:

GPE = FMm/r

btw i have seen GPe referred to as gravitational binding energy in this case..might help

Reply 1

Theorist

It doesn't. It goes to

\displaystyle \frac{G m M}{r}.

But if you mean what I said above then there's two ways to answer this. The A-level way is just

W = Fs.

Use Newton's Law of Gravitation for the force and remember that the distance in this scenario is the radius

r.

The formal way is to integrate the gravitational force (again from Newton's Law) with respect to

r

but between the upper and lower limits of infinity and

r

respectively.

This Wikipedia article will explain all.

Reply 2

Sinay

lol thank you so much - sorry about the mistake in the formula

No problem. :smile:

The A level way is NOT to use W = Fs

This is nonsense as the force varies with r

the gain in GPE is equal to

m \Delta V

and as V at infinity is zero

\Delta V

is just equal to V at the surface of the earth where

V = -\frac{GM}{r}

Reply 5

Theorist

My bad. Thanks for correcting me Drummy. :smile:

Reply 6

Drummy

np m8

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