# Help with a Proof

1. Oct 16, 2004

### decamij

How can i mathematically prove the following equation:
I have to prove that the minimum speed required to maintain orbit around the Earth is (given the mass of the earth and universal gravitation constant)

v = 2.00x10^7
(root)r

I have to basically prove this equation:

v = GmE
r

P.S. the whole equation to the above is square rooted, and the r should be UNDER GmE).

2. Oct 16, 2004

### Clausius2

In order to mantain the equilibrium of the body the centrifugal force has to be equal to the gravitational one:

$$m\frac{v^2}{r}=\frac{GMm}{r^2}$$

$$v=\sqrt{\frac{GM}{r}}$$

3. Oct 16, 2004

### decamij

So if this were a question on an assignment out of 6 marks, all i would have to is show the relationship between the two equations (it would be a pretty short proof). Thanx a lot