I will certainly have a look around.
Sent: 12/04/2017 08:52:26 GMT Daylight Time
Subj: Re: Velocity and Radius
The problem is that I could not find any information on radius of the OJ287 system at all. Perhaps you can give it a try.
Am 12.04.2017 um 09:48 schrieb EMyrone:
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.
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.
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.