Talk: Kepler's laws of planetary motion

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Hi,

I find this article, and particularly the "proofs" to be very misleading. The proofs assume that Newton's laws are correct, and then show that Kepler's laws are correct because a body moving according to Newton's formula do indeed move according to the laws of Kepler.

It should be the other way around.

Kepler and Brahe made observations about the position of planets around the sun, and plotted them on a map. Kepler found regularity in the planet's movements, which he expressed as his three laws. The three laws may be "proven" by making previsions about a planet's future position, and verify those predictions.

Later, Newton came with his law of gravitation, that he developed from Kepler's laws. Newton's law says "in order for planets to move according to Kepler's laws, they must be attracted to each other by a force ... etc ..." So, of course, Newton's equations do describe the Kepler's laws. They were made to do so !

--Stephan Leclercq 10:41, 28 Aug 2004 (UTC)

This historical comment deserves to be in the article

The above comment by Stephan deserves to be in the article: how did Kepler, thanks to his observations, came to find his 3 laws, then how these laws where used by Newton to find the Law of Gravitation in 1/r^2 ... that is effectiveley made from the law of Kepler. Thanks --Nicop 19:25, 21 Oct 2004 (UTC)

Dependence on spatial dimensions

Assuming that <math>\mathbf{g}=-\nabla U<math> and that <math>\mathbf{g}<math> is divergence-free, i.e <math>\nabla^{2} U = 0<math>, in <math>N<math> spatial dimension the potential satisfies <math>U(r)=C/r^{N-2}<math>. Hence in order to obtain circular and elliptic orbits, <math>N<math> has to be <math>3<math>.