I would suggest starting the analysis by using the astronomically measured perihelion radius of planets of the solar system. This is probably known with great precision for every planet. Then use the classical approximation:
v squared = MG ( 2 / r – 1 / a)
where r is the radius at the perihelion and a the semi major axis, MG neing known with great precision where M is the mass of the sun. Use astronomical tables to find
a = alpha / (1 – eps squared)
in the classical approximation. Here alpha is the half right latitude and epsilon the eccentricity. Another method would be to use r at the perihelion and use the relativistic orbital velocity:
v = gamma (X dot squared + Y dot squared) power half
having found X dot and Y dot from integrating the relativistic equations of motion numerically.
I think that these data may be available for some systems of massive m and M. I will have a look with google for binary pulsars such as the one used in UFT106 ff, the Hulse binary pulsar.
Sent: 11/04/2017 21:53:20 GMT Daylight Time
Subj: Re: Google Search on the Formation of Super Massive Binaries
Is anything known about the distance of OJ287 or S2 (near to our galaxy centre) from their central parrtner? We are in the dilemma that the calculation only needs an initial radius and velocity, but these parameters seem to be difficult to obtain. There are rather guesses on ellipticity and orbiting time, but these are of less use for a first-principles calculation and ellipticity is not well defined for an orbit not being an exact ellipse.
Am 11.04.2017 um 10:46 schrieb EMyrone:
Google “largest observed orbital precession” to find a site called “biggest black hole in the cosmos discovered”. In ECE2 the concept of black hole is abandoned, the mass is simply a super heavy mass. In Quasar OJ287 a mass m orbits a mass M every twelve years. M is 18 billion sun masses, and mass m is 100 million sun masses. The orbital precession is 39 degrees per orbit, and the orbit is decreasing. With the new lagrangian method it should be possible to explain this orbit straightforwardly. The first task is to give an analytical expression for the precession per orbit. Then modify the potential so that the orbit decreases. Then google “binary black holes evolution” to find the system GW150914. In the standard model this was used to claim gravitational radiation but this claim is rejected in ECE2 because the UFT papers have shown in many ways that the Einstein theory is incorrect. Stephen Crothers has also criticizsed black holes and gravitational radaition using his own internationally well known arguments. One site claims that the supermassive binary system is formed from massive stars that are formed very close together and orbit each other in only a few days. The obsolete standard theory claims that there is no mass transfer. So this gives a clue as to initial conditions. AIAS Fellows are enouraged to google around to try to find more data of this kind.