This looks full of interest, bearing in mind that we are using a theory with no adjustables and based on one lagrangian.
Sent: 12/04/2017 15:28:36 GMT Daylight Time
Subj: Re: Data on the Hulse Taylor Binary Pulsar PSR 1913 + 16
I did a simulation for the Hulse-Taylor binary system so I had useable initial conditions. I think I computed the initial velocity from the angular momentum. Will look into this on Friday or Saturday.
Am 12.04.2017 um 13:00 schrieb EMyrone:
These were first analysed in UFT106. Google “perihelion binary pulsar” to find that in this pulsar, two heavy stars of almost equal mass orbit a common centre of mass in 7.75 hours. They weigh 1.4 solar masses. The minimum separation is called the periastron, and is 1.1 solar radii. The maximum separation or apastron is 4.8 solar radii. Google “perihelion of binary star systems” to find that the orbital eccentricity is 0.62. The observed periastron advance of the binary pulsar is 4.2 degrees per year. The non relativistic lagrangian is described in Marion and Thornton, chapter 7, p. 245, third edition, Eq. (7.4)
Lagrangian = (1/2) mu v bold dot v bold – U(r)
where the reduced mass is
mu = m1 m2 / (m1 + m2)
where m1 is about the same as m2. Here:
U(r) = – m1 m2 G / r
r = modulus ( r1 bold – r2 bold)
and r1 bold is the vector from the center of mass to m1, r2 bold is the vector from the centre of mass to m2. The perisatron is defined by the minimum value of modulus r1 bold minus r2 bold. So I suggest setting up the initial condition at the periastron, where r is known and proceed to compute X dot and Y dot and calculate the initial relativistic orbital velocity. The orbit should look like a rosette and should advance by 4.2 degrees a year. By “year” I assume that is meant is the orbital interval of 7.75 hours. The orbit also shrinks, and in UFT106 – UFT108 extensive calculations and computations were made.