Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Metric matrix for binary star system?

  1. Mar 7, 2015 #1
    What does the metric matrix look like for a binary star system? Does each follow its usual geodesic about the other? It seems like the solution would have to be different somehow than that for a tiny planet circling a big sun.
     
  2. jcsd
  3. Mar 7, 2015 #2

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    There isn't any exact 2-body metric in GR. We do have an approximate metric for the n-body solar system, though, based on the theory of harmonic coordinates. I think it is of order 1.5. A terse and not terribly understandable presentation of the resulting metric can be found in the IAU (International Astronomical Union) resolution B1.3 for the year 2000, see for instance http://syrte.obspm.fr/IAU_resolutions/Resol-UAI.htm. There are a variety of sources that try to explain the resolution in more detail. See for instance "THE IAU 2000 RESOLUTIONS FOR ASTROMETRY, CELESTIAL MECHANICS, AND METROLOGY IN THE RELATIVISTIC FRAMEWORK: EXPLANATORY SUPPLEMENT", http://iopscience.iop.org/1538-3881/126/6/2687/fulltext/202343.text.html. The "explanations" are still not light reading.

    An earlier (I forget the year) IAU version had a scalar gravitational vector potential u, which can be thought of as the Newtonian potential, defined by a Newtonian-like integral, and a set of corresponding metric coefficients. It is rather similar to the PPN formula you'll find in many papers and textbooks. The year 2000 version has a 4-vector potential, broken down by the resolution into a scalar part w, and a 3-vector part ##w^i##. The metric coefficeints are are written as functions of u (in the simple earlier version), and the 4-potential ##(w, w^i)## in the current 2000 version. There are already papers that discuss higher-order, higher accuracy approximations for some upcoming experiments
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Metric matrix for binary star system?
Loading...