Will there be planetary type motion possible if force varies linearly or cubically with distance?
If a body is revolving around another body then can i say with total confidence that the body is experiencing inverse square force?
Hi Vikash,
The answer to your question is given by Bertrand's theorem which states that there are only two central forces that lead to closed orbits. F~1/r2 and F~-r. The first force leads to Kepler's law, the second one to a radial harmonic oscillator (https://en.wikipedia.org/wiki/Bertrand%27s_theorem).
Cheers
No you cannot conclude that it is an inverse square law. If the body is revolving around another body orbits need not to be closed, but can stay finite.For other potentials the orbits can remain between rmin and rmax. See for instance Mechanics, by Landau and LIfhsitz, or Classical Mechanics, by Goldstein for an extensive discussion of the possibilities. For 1/r potentials conical intersections (circle, ellipse, parabola and hyperbola), are the only possibilities. In reality it is more complicated due to tidal forces and general relativity.
By the way: a body does not revolve around another body, they both revolve around their center of mass.
Would electrons orbiting a nucleus be an example of an orbiting body based on non-gravitational forces?
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