S2 Star System

Agreed with all these ideas, especially if the large precession of the S2 star is known accurately. I will work on the relativistic lagrangian for the Hulse Taylor system. A peaceful Easter!

To: EMyrone@aol.com
Sent: 15/04/2017 19:40:36 GMT Daylight Time
Subj: PS: Calculation of double star systems with reduced mass

PS: I tried some numerical runs. It is difficult to reproduce the orbit period of about 27 000 s. It only works with an adopted initial velocity. It seems that the eccentricity comes out too small then. I have still to extend the code to extract this.

Besides this, I wonder if the reduced mass method is applicable at all in the relativistic case. The relativistic Lagrange term is non-linear so that the method of Marion and Thornton will not work. Perhaps we should switch to a 2-body calculation which is unproblematic in the kinetic energy terms. Only the potential energy terms become more complicated, but probably handable by Maxima.

A third alternative would be to first switch over to the S2 system where precession is much larger so that we could have a direct chance with our numerical method. If it works, we could come back to the Hulse-Taylor pulsar afterwards.

I am stopping here for the Easter break.

Horst

Am 15.04.2017 um 20:08 schrieb Horst Eckardt:

The introduction of the reduced mass leads to the effect that it does not cancel out in the Euler-Lagrange equations. Insertion of the term for the reduced mass mu leads to an effective potential term

U(r) = -(m_p + m_c) * G/r.

The relativistic Lagrange equations are:

The observations relate to the ellipses of each star partner. Their coordinates are r1 and r2, and not the reduced coordinate r. Therefore the observed values have to be transformed to r according to

bold r = (m_p + m_c) / m_c * bold r_p.

These initial positions can be inserted into the calculation. What happens with the velocities? It seems that because of

bold v = bold r dot

also the velocities have to be transformed.

Horst


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