Why is the gravitational potential not zero at the neutral point?

[nokia8650]

The image below shows a sketh of gravitation potential (y axis) vs. position:

http://img175.imageshack.us/img175/5717/60413547vb3.th.jpg

Can someone please explain why the potential does not equal zero at the neutral point - wouldn't the two potentials cancel each other out?

Thanks

 

[D H]

Can someone please explain why the potential does not equal zero at the neutral point - wouldn't the two potentials cancel each other out?

First off, why would you expect it to go to zero? That plot is of

$$u(r) = -\left(\frac{GM_e}{|r|} + \frac{GM_m}{|R_m-r|}\right)$$

That function is negative definite: its value is negative for all finite values of r.


Secondly, what do you mean by "neutral point"? This term has multiple meanings.

 

[tiny-tim]

The image below shows a sketh of gravitation potential (y axis) vs. position:

http://img175.imageshack.us/img175/5717/60413547vb3.th.jpg

Can someone please explain why the potential does not equal zero at the neutral point - wouldn't the two potentials cancel each other out?

Thanks

Hi nokia8650!

Where is the potential being measured from (in other words, where is zero potential)?

Potential is often measured "from infinity" …

in that case, the potential will only be zero at an infinite distance from both the Earth and the Moon.