# Inverse square law and Kepler's third law

Andrew Mason
Homework Helper
Reshma said:
Also note, Kepler's third law is rigorously true for the electron orbits in the Bohr atom (Source: Classical Mechanics: Herbert Goldstein).
In the Bohr atom the force on the electon is a central force that varies as 1/r^2. That gives you Kepler's third law. But the Bohr atom is not an accurate model of physical reality.

AM

Andrew Mason said:
In the Bohr atom the force on the electon is a central force that varies as 1/r^2. That gives you Kepler's third law. But the Bohr atom is not an accurate model of physical reality.

AM

Ah finally someone hits the nail on the head. You see its like this: you start out with an assumed model of the motion. Then you use some other "laws" or "ideas" to show that something (which you're trying to show) holds 'rigourously'. But the assumption need not be correct in real life as Andrew has so rightly pointed out. As for reality, there are perturbations in orbits due to several reasons. In a crude way perhaps it is right to say that a perturbation term (which cannot be correctly described in our world) gets added to the differential equation of every point motion referred to an inertial or noninertial frame. For all practical purposes in undergraduate studies, this term equals zero.

Now, regarding the book reference, to be honest I haven't even heard of this book by AS Ramsey. I was referring to Mechanics by AS Ramsey parts I and II (sections on Central Orbits/Polar Orbits).

Cheers
vivek