Quick Check

359(7): A New and General Orbital Dynamics

October 16, 2016

This is given by the new orbital law (4), the orbital acceleration due to gravity (or force between an object m orbiting an object M) is the convective derivative of the orbital velocity of m about M. It is illustrated for planar orbits in the XY plane and for the Newtonian acceleration due to gravity.”

It seems to us that your equation 4 cannot be reconciled with the fundamental dynamic orbital invariant (which also applies to the Bohr atom),

L^2 = GMm^2k

where L, M and m have their usual meanings and k is the length of the semi-focal axis. Of course, you will not be familiar with the above expression because it is missing from standard physics textbooks such as Goldstein … so how can you fiddle your calculations to match laws that you do not even know about? Of course, our conclusion hinges on what g is supposed to be. It is usually the value of gravitational acceleration at a planet’s surface, but your use of it is rather vague.

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