413(6): Orbital Shrinkage Equation

Many thanks, the orbital shrinkage can be plotted from Eq. (11) and comes directly from L = m r squared d phi’ / dt. The coordinate system is changed from (r , phi ) to (r, phi’) where phi’ = phi + omega sub 1 t. In the hamiltonian, phi is changed to phi’. This results in Eq. (14), in which the alpha and epsilon are defined with phi replaced by phi’. A useful rule is that whenever phi occurs in any calculation or situation, it is replaced by phi’, but r remains unchanged. The Lagrangian calculation is also correct, it is equivalent to the hamiltonian calculation and leads again to Eq. (14). I agree that r(t) defined by phi and r(t) defined by phi’ are different. The orbit is also defined by phi replaced by phi’, leading to Eq. (14). So we simply plot alpha versus t from Eq. (14). The answer to the mystery is that alpha, the half right latitude or semi latus rectum of a shrinking ellipse, also shrinks with time according to Eq. (14). The cosine function in Eq. (14) is always greater than or equal to – 1 and less than or equal to 1 as time t goes to infinity. However, as time t goes to infinity, r shrinks to zero and so alpha / (1 + epsilon cos phi’) shrinks to zero. The quantity omega = d phi / dt is defined with phi (i.e. equivalent to omega sub 1 goes to zero, or no frame rotation) , giving the angular momentum L sub 0 when there is no rotation.

Re: 413(6): Orbital Shrinkage Equation
To: Myron Evans <myronevans123>

PS: Isn’t omega be observed in the observer system? Then it could not be
identified with L_0 as in eq. (8), or am I wrong?

Horst

Am 28.08.2018 um 12:13 schrieb Myron Evans:
> The shrinkage is expressed most clearly through equations (11) and
> (12), in which r can be plotted against t, resulting in Eq. (12). The
> shrinking orbit is then Eq. (14), from which the half right latitude
> can be plotted as a function of t. The orbit is given correctly by
> both the lagrangian and hamiltonian methods, so all is self
> consistent. The dependence of r on time of a binary pulsar can be
> measured in astronomy and the ECE theory compared with the data.


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