Integrating the gravity formula?

[Mr Davis 97]

I decided to integrate the formula $g = \frac{GM}{r^{2}}$, and I ended up getting $v_{g} = -\frac{GM}{r}$. What is the meaning of the latter formula, and is it useful in anyway?

 

[axmls]

It's equivalent to the gravitational potential (not the gravitational potential energy). In other words, if you're familiar with electromagnetism, it's analogous to the electric potential V. Multiplying by a second mass will give you the gravitational potential energy, and then taking the derivative after that will give you the force. Taking the derivative of what you have now would give you your original relationship, which is the strength of the gravitational field.