# Thread: How do gravitational force lines work?

1. I was thinking. Let’s say you want to work out the gravitational attraction between two spheres. So you use the formula F = Gm1m2/r^2. That means you take it as if each body is attracted towards a point mass r distance away. But when you think about it, the resultant force coming from the mass at the horizons would have to be converted with Pythagoras to get the linear attraction in the direction of the centre of mass. Also, the other side of the body is farther away from you than the closer part. So how does that work? Does it all cancel out exactly as if Pythagorean conversions of the field lines were done from all points on each body? Maybe a stupid question :?

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3. I suppose its like rolling down a hill, it doesn't matter which side you are on of the hill you will reach the middle at the same relativistic time :?.

4. Originally Posted by KALSTER
I was thinking. Letâ€™s say you want to work out the gravitational attraction between two spheres. So you use the formula F = Gm1m2/r^2. That means you take it as if each body is attracted towards a point mass r distance away. But when you think about it, the resultant force coming from the mass at the horizons would have to be converted with Pythagoras to get the linear attraction in the direction of the centre of mass. Also, the other side of the body is farther away from you than the closer part. So how does that work? Does it all cancel out exactly as if Pythagorean conversions of the field lines were done from all points on each body? Maybe a stupid question :?
I can't do the maths myself, but that was one of Newton's triumphs. He demonstrated that, for a perfect sphere, the gravitational force acted exactly as though it were all concentrated at the single central point.

By all accounts he invented the calculus in order to solve problems like this, although when he presented his findings (in his famous Principia) he derived his results using classical (Euclidean) geometry. I think the first step towards understanding it is the consideration of a solid sphere as a series of infinitesimally thin concentric shells. Try to imagine what the point (Centre of Gravity) for any given shell might be.

5. In a perfect sphere, wouldnt the center point stay the same no matter which concentric circle you use for measuring?

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