# Gravity of single body

1. Jan 20, 2009

### chis

Sorry to ask such a simple question but I appreciate the level of knowldege you guys have.
What is the equation for calculating a single bodies gravity?

2. Jan 20, 2009

### mgb_phys

The gravitational field strength is = GM/r
(in classical gravity - it's a bit more complicated in general relativity)

It's really just a different way of writing the equation in the other thread for the force on a 1kg object placed at a distance 'r'

3. Jan 20, 2009

### chis

Is r measured from the centre of the object? If so is gravity stronger closer to the centre of the earth.
Thanks by the way
Chris

4. Jan 20, 2009

### mgb_phys

Yes The nice thing about Newton's gravity is you can just use the total mass at the 'centre of gravity' and not have to care about the shape or distribution.
The earth could actually be hollow and as long as it had the same total mass you wouldn't be able to tell - gravity would work just the same.

5. Jan 20, 2009

### chis

So at the centre of an object the value r = 0

6. Jan 20, 2009

### Nabeshin

While in Newtonian gravity you treat all an object's mass as if it were located at the center, this assumption is only valid while you are outside of the body. If, for example, you started digging into the earth, you would find that the gravitational force decreases to zero as you approach the center.

7. Jan 20, 2009

### chis

Is there an equation tht reflects this?

8. Jan 20, 2009

### Staff: Mentor

Furthermore, it's only valid for spherically symmetric mass distributions.

9. Jan 20, 2009

### Nabeshin

Assuming a uniform spherical mass distribution, we have the following equations:

$$g(r)=-G\frac{m}{r^{2}}\hat{r} ; r>r_{0}$$
$$g(r)=-\frac{Gm_{0}}{r_{0}^{3}}r\hat{r} ; r<r_{0}$$