# Diminishing Gravitational Acceleration with Distance

1. Apr 15, 2010

### cbd1

I'm wondering what the equation is that shows how a gravitational field diminishes with distance from the object of mass. I would be looking for an equation showing the difference in the value of gravitational acceleration at points in space with increasing distance from the body. Would this be shown with a differential equation?

2. Apr 15, 2010

### Superstring

$$g = \frac{GM}{(R + h)^2}$$

Where G is the gravitational constant, M is the mass of the gravitating body (the Earth for example), R is the radius of the body (radius of the earth for example), and h is the height above the surface of the body.

3. Apr 15, 2010

### AndyK

GMm
----- or (GMm)/r^2
r^2

is the formula for the gravitational force. G is the gravitational constant, M is the mass of one object, m is the mass of the other object and r is the distance between the two. r is measured from the center of mass of the both objects so my r equals Superstrings (R+h), and it only works if both objects are pretty much spherical or one of the objects is really small in relation to the other, as an example you and the earth, it can be assumed that you are a point mass in respect Earth. If these conditions are not there, you need to use integration.

A short answer to what you are asking would be, the gravitational force is inversely related to the square of the distance between the two objects. It is the magical 1/r^2 relation which also shows up in Coulomb's law in electrostatics. As an example if you doubled the distance between 2 objects, you would lessen the gravitational force by 4 folds. Edit: I have re-read your topic and if you need to also talk about acceleration then you need to get Newton involved with the F=ma. F would be GMm/r^2, m's will cancel on both sides and acceleration will equal to what superstring wrote on his post. Therefore the acceleration would also be cut down by 4 times.

Ps: Superstring how do u post your equations like that? I'd like to learn.

Last edited: Apr 15, 2010