# Gravitational Potential Energy of the earth

kt102188

## Homework Statement

How high above the surface of the Earth must a mass be located so its gravitational potential energy is only 17.00% of its value on the surface?

## Homework Equations

PEg=(-GMm)/r, PElocal= mgy where y is height the object can fall

## The Attempt at a Solution

I've tried a couple of different things but all my variables cancel out.

(-GMm)/r1=0.17((-GMm)/r2

r1/0.17=r2 If I randomly set r1 to be 1 r2= 5.88235 but that doesn't make sense because if you raise an object by 5m it would have a greater PEg

Any suggestions on where to go?
Thanks!!

## Answers and Replies

Homework Helper
Welcome to PF!

Hi kt102188! Welcome to PF! r1/0.17=r2 If I randomly set r1 to be 1 r2= 5.88235 but that doesn't make sense because if you raise an object by 5m it would have a greater PEg

But the radius of the Earth is a lot larger than 1m. (and remember, the question assumes that the PE at ∞ is zero )

kt102188
Thank you! I was totally thinking of this wrong. Actually using the radius of earth got the right answer.