I have a couple questions on gravity

Darkroman

My physics knowledge is barely 101 so bare with me. However I've always wondered about gravity, just never took much time to look it up. I was hoping you could help me out a bit on it, perhaps give me some internet links to learning resources.

Is there an equation to state (let's say an ideal or perfect celestial sphere about 10,000 miles in diameter, and density is on the order of 2) how much gravity it has (or is it better to say how much it curves spacetime)?

Can you make a connection between the mass an object has with the amount of gravity? How about density?

Thanks in advance.

mikeph

Yes. The gravitational field due to a point mass (in units of acceleration) is -GM/r^2. Any massive object with a spherically symmetric mass density distribution (eg. a planet or a star) can be modelled as a point mass at the centre of the sphere so that you can use this equation (as long as r > radius of the body).

That's the Newtonian (classical) theory. I don't suggest learning Einstein's version before this.

rbnvrw

So, if you want to calculate the gravitational force a massive object of mass [itex]M[/itex] exercises on some other mass [itex]m[/itex], it would be done like this:
[itex]F_G = -G\frac{mM}{r^2}[/itex]. Where [itex]F_G[/itex] is the gravitational force, [itex]G[/itex] the gravitational constant and [itex]r[/itex] the distance between the two objects. (either as size or vector)
If you only know the density of the object, you can calculate the mass like this:
[itex]{\int\int\int}_V \rho(x,y,z) dV[/itex] or, if the density [itex]\rho[/itex] is constant: [itex]\rho \times V = \frac{4}{3} \pi R^3 \rho[/itex]
Hope this helps!