How to use S-metric to periastron precession of binary stars

• Vincentius
In summary, the conversation discusses the use of the Schwarzschild metric to calculate the precession of an elliptic orbit around a large central mass, with the condition that the particle's mass is much smaller than the central mass. However, in the case of binary stars, this condition is not met and the sum of the two stars' masses must be used as the central mass in the calculation. This is known as the two-body problem in general relativity and there is no known analytical solution. Some references on this subject are provided for further reading.
Vincentius
The Schwarzschild metric allows to calculate the precession of an elliptic orbit of a particle around a large central mass, provided the mass of the particle is much smaller than the central mass M. This condition is not met in the case of binary stars m1 and m2 revolving around each other.
There is mention of a possibility of still using the Schwarzschild metric, but then one must take the sum of the masses of the two stars for the central mass, i.e. M=m1+m2.
I can imagine this works, but don't know how. Could anyone supply a reference on this subject.
Thanks!

Yes, I know there is no analytical solution, that's why I asked about the approximation using M=m1+m2. But I cannot find a derivation of this approximate solution. Can anyone help out? Thanks

Vincentius said:
Yes, I know there is no analytical solution, that's why I asked about the approximation using M=m1+m2. But I cannot find a derivation of this approximate solution. Can anyone help out? Thanks
This is the only paper on this subject I've got - arXiv:gr-qc/0502062v1 14 Feb 2005.

1. What is the S-metric and how is it used to measure periastron precession of binary stars?

The S-metric is a measure of the curvature of space-time around a massive object, such as a binary star. It is calculated by looking at the shift in the wavelengths of light emitted by the stars due to their motion. By analyzing the S-metric, scientists can determine the amount of precession (change in the orientation of the stars' orbits) occurring in the binary system.

2. How accurate is the S-metric in predicting periastron precession of binary stars?

The S-metric is a very accurate tool for measuring periastron precession in binary stars. It has been used by scientists for decades and has been tested and verified through numerous experiments and observations. However, it is important to note that other factors, such as the presence of other massive objects in the system, can also affect periastron precession.

3. Can the S-metric be used for all types of binary star systems?

Yes, the S-metric can be used for all types of binary star systems as long as they are observable. This includes both visual binaries (where the stars can be seen separately) and spectroscopic binaries (where the stars appear as one point of light, but their spectra can be analyzed separately).

4. How does the S-metric compare to other methods of measuring periastron precession?

The S-metric is considered to be one of the most accurate methods for measuring periastron precession in binary stars. Other methods, such as timing the eclipses of the stars or studying their radial velocity, can also provide valuable information, but they may be affected by other factors and are not as precise as the S-metric.

5. Are there any limitations to using the S-metric for measuring periastron precession?

One limitation of using the S-metric is that it requires precise measurements of the stars' positions and velocities, which can be difficult to obtain. The S-metric also assumes that the stars are in a perfect circular orbit, which may not always be the case in reality. Additionally, the S-metric cannot be used for systems where the stars are too close together or where the signals from their spectra overlap too much.

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