Calculating Gravity of a Single Body: Equation and Explanation

[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?

 

[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'

 

[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

 

[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.

 

[chis]

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

 

[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.

 

[chis]

Is there an equation tht reflects this?

 

[Doc Al]

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.

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

 

[Nabeshin]

Is there an equation tht reflects this?

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

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