Discussion of Note 365(5)

Many thanks, such an analysis would be very useful. Complexity is no problem for the computer and the results are greatly clarified by a graphical analysis.

To: EMyrone@aol.com
Sent: 06/01/2017 17:44:57 GMT Standard Time
Subj: note 365(6)

The result of the iterative scheme depends on the functional dependences
assumed. First I checked that inserting the Newtonian orbit (eq. 2 with
Omega=0) gives the Newtonian force law. The result is

F(r) = – L^2 / (alpha m r^2)

which seems to be correct.

Assuming a constant Omega in (2) and inserting (2) in (1) gives the
force law (6) again, but with precessing orbit (2). This seems plausible.

More interesting cases are for non-constant Omega. I am not sure how the
theta derivative in (1) should be handled. Omega only depends on r, but
r depends on theta via the orbit, so Omega depends indirectly on theta:

Omega(r(theta)).

Since the total derivative appears in (1), not the partial derivative, I
assume that the theta dependence in Omega has to be propagated. This
then gives very complicated expressions in the Binet equation (1). I can
do a graphical evaluation.

Horst

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