I would suggest using the radius at the perihelion (closest approach). In the classical approximation this is r = alpha / ( 1 + epsilon). The astronomers usually give alpha and epsilon. The orbital velocity is the relativistic velocity:

v = gamma (X dot squared + Y dot squared) power half

If the code gives X dot and Y dot then v can be calculated. To start with the parameters which you used to get a precessing ellipse can be adjusted to give a precession of 39 degrees per orbit. I agree that the problem could be worked out entirely without adjustables. To start with data can be used in the solar system, where orbits are known with precision, r is known at the perihelion, and M is the mass of the sun.

To: EMyrone@aol.com

Sent: 11/04/2017 19:54:05 GMT Daylight Time

Subj: Re: PS Numerical Estimate of the Precession in Quasar OJ287

The precession angle per orbit must be determined by some additional code from the numerical solution. The relativistic method is a first-principles method in the sense that no adjustable parameters are needed. We need the orbital radius and the velocity of the mass m at a certain point of time. If M is not known, we can use it to adjust the precession angle to the observed value.

Horst

Am 11.04.2017 um 10:58 schrieb EMyrone:

With such a large precession of 39 degrees per orbit, many orders of magnitude bigger than in the solar system, it should be possible to adjust conditions to use the experimentally observed mass M to find the precession numerically, and to measure it graphically. The new equation of motion is:

r bold double dot = (gamma MG / r cubed) ( v bold (v bold dot r bold) / c squared – r bold

so only M is used. Here gamma is the Lorentz factor. It is not clear how the astronomers estimated M. The above equation can be used to find M by matching the experimentally observed precession of 39 degrees per orbit to the theoretical result. The equation is not soluble analytically but this is no problem because the numerical solution is very precise.

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