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#1




OJ287 binary black hole system perihelion shifts
I calculated OJ287 binary black hole system with Swarzshild General Relativity system and I got two different perihelion shift values (not rounded numbers): 27.73298398 degrees and 27.79877741 degrees per one orbit. I got two analytic solutions also but above was calculated with primary solution. Ref. Lankeswar Dey et al. 2018. The Astrophysical Journal. 866:11 (20pp), 2018 October 20. Table 2/page 7. Best Regards, Hannu Poropudas, Finland.

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#2




OJ287 binary black hole system perihelion shifts
I give here those two analytic solutions:First primitive function is following:e=2.117198112*EllipticF(sin(P),0.2601014 318), r=(0.1627132736e34*sin(P)^20.2405124138e35)/(0.2726824096e18*sin(P)^20.3378949220e18), definition areas are 0=P=Pi/2 and 0.7117964733e17=r=0.3438620569e18. Second primitive function is following: ee=2.117198112*EllipticF(sin(P),0.9655812990), rr=(0.2051871297*sin(P)^2)/(0.5967134948e16*sin(P)^2+0.3378949220e18), definition areas are 0=P=Pi/2 and 0=rr=0.5967134948e16. Maple 9 used and cgs unit system with c=1 Weinberg's used units. Best Regards Hannu Poropudas, Finland

#3




OJ287 binary black hole system perihelion shifts
I forget to mention that full orbits in both General Relativity analytic solutions are achieved when one takes + and  signs for first +e and second +ee elliptic integrals of second kind. Remark that Maple9 uses eletter in those formulae as 10^ meaning also, not to confuse about this. Best Regards, Hannu Poropudas, Finland

#4




OJ287 binary black hole system perihelion shifts
Elliptic integral of the kind was corrected name. When plotting coords=Polar, Maple 9 uses this for polar coirdinates. Best Regards, Hannu Poropudas, Finland.

#5




OJ287 binary black hole system perihelion shifts
Elliptic integral of the first kind was correct name. Plotting is done in polar coordinates. Best Regards, Hannu Poropudas, Finland.

#6




OJ287 binary black hole system perihelion shifts
I have used P^2=(4*Pi^2*a^3)/(G*M) to calculate semimajoraxis a, with P=12.062 yr and M=18348*10^6*M_SUN. But z=0.306 From 2014 Thesis of Pihajoki P. University of Turku, ser. A1  492. Annales Universitatis Turkuensis. If I would take this redshift into account should I recalculte all by P=12.062yr/(1+0.306)=9.235834609 yr? (I use not rounded numbers. Hannu

#7




OJ287 binary black hole system perihelion shifts
I recalculated with accounting z=0.306:e=2.142521522*EllipticF(sin(P),0..28770946 99), definition areas are 0=P=Pi/2 and 0.5957449715e17=r=0.2877986650e18. r=(0. 1389227423e34*sin(P)^20.1678282376e35)/(0.2282241678e18*sin(P)^20.2817115471e18). Second analytic slution: ee=2.142521522*EllipticF(sin(P),0.9577177353), rr=(0. 1751864413e34*sin(P)^2)/(0.6087117927e16*sin(P)^2+0.2817115471e18), definition areas are 0=P=Pi/2 and 0=rr=0.6087117927e16. Problem with calculation precession angle per orbit in first parametric formula which gives Imaginary number for P which corresponds aphelion. P=1.570796370.1503825754e4*I,and P=1.570796327+0.1503825754e4*I,Maple 9 gives or these 34.01372910 degrees per orbit and 34.04443070 degrees per orbit. Best Regards, Hannu Poropudas, Finland.

#8




OJ287 binary black hole system perihelion shifts
J=  1.731669280*10^16 total angular momentum per unit mass and E= 1.015569493 total energy per unit mass. Weinberg gives in his book p. 187 formula for dP/dt = J*(12*M*G/r)/r^2, M=3.648591540*10^43 g. G=6.674083100*10^(8), c=1 and cgs units. I give this due orbit seems to be strange pendulum orbit with no proper aphelion. Best Regards, Hannu Poropudas, Finland.

#9




OJ287 binary black hole system perihelion shifts
Not dP/dt. Correct is de/dt. Hannu

#10




OJ287 binary black hole system perihelion shifts
Not dP/dt. Correct is de/dt. Sorry, Hannu


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