# Potential energy of earth and gravity

1. Feb 17, 2014

### Bandarigoda

Assume earth's radius R and there is a mass m. We put that mass in height of R from the earth's surface. I want to calculate it's potential energy.

I calculated it and got mgR/4 but my teacher said the answer is mgR/2 . Why my answer is wrong?

I just calculated the gravity in the height of R and applied it to e = mgh

2. Feb 17, 2014

### tiny-tim

Hi Bandarigoda!
??

(and at that distance you can't treat gravity as constant)

3. Feb 17, 2014

### voko

Either answer can be right or wrong, depending on where the potential energy is supposed to be zero. Unless you fix that, the discussion is meaningless.

4. Feb 17, 2014

### Bandarigoda

Here

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5. Feb 17, 2014

### Enigman

You are assuming zero potential energy at the surface of earth while your teacher's doing it at infinity. Both answers are correct but at these distances infinity is usually used.
Your teacher is using the formula:
$$U= \frac {Gm_1m_2}{R}$$ [edited]
Assuming U=0 at R=$\infty$

Last edited: Feb 17, 2014
6. Feb 17, 2014

### tiny-tim

ahhh now i understand …

you've correctly found the different values of g(r) (as a function of radial distance r),

but then you've used mgh (= mg(r - R)) for potential energy,

7. Feb 17, 2014

### Bandarigoda

Oh thank you very much guys. I got it now.

8. Feb 17, 2014

### tiny-tim

for the record: that should be
$U= -\frac {Gm_1m_2}{R}$

9. Feb 17, 2014

### Enigman

Uncaffeinated brain fart.