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Gravity waves

  1. Jun 14, 2013 #1

    wolram

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    From Wiki.
    The pulsar and its neutron star companion both follow elliptical orbits around their common center of mass. The period of the orbital motion is 7.75 hours, and the two neutron stars are believed to be nearly equal in mass, about 1.4 solar masses. Radio emissions have been detected from only one of the two neutron stars.
    The minimum separation at periastron is about 1.1 solar radii; the maximum separation at apastron is 4.8 solar radii. The orbit is inclined at about 45 degrees with respect to the plane of the sky. The orientation of periastron changes by about 4.2 degrees per year in direction of the orbital motion (relativistic precession of periastron). In January 1975, it was oriented so that periastron occurred perpendicular to the line of sight from Earth.[2] [5]
    The orbit has decayed since the binary system was initially discovered, in precise agreement with the loss of energy due to gravitational waves predicted by Einstein's general theory of relativity.[2][5][6][7] The ratio of observed to predicted rate of orbital decay to be 0.997±0.002.[7] The total power of the gravitational radiation (waves) emitted by this system presently, is calculated to be 7.35 × 1024 watts. For comparison, this is 1.9% of the power radiated in light by our own Sun. (Another comparison is that our own Solar System radiates only about 5000 watts in gravitational waves, due to the much larger distances and orbit times, particularly between the Sun and Jupiter).
    With this comparatively large energy loss due to gravitational radiation, the rate of decrease of orbital period is 76.5 microseconds per year, the rate of decrease of semimajor axis is 3.5 meters per year, and the calculated lifetime to final inspiral is 300,000,000 years.[2] [7]
    Mass of companion: 1.387 MSun
    Orbital period: –7.751939106 hr
    Eccentricity: –0.617131
    Semimajor axis: 1,950,100 km
    Periastron separation: 746,600 km
    Apastron separation: 3,153,600 km
    Orbital velocity of stars at periastron (relative to center of mass): 450 km/s
    Orbital velocity of stars at apastron (relative to center of mass): 110 km/s
    In 2004, Taylor and Joel M. Weisberg published a new analysis of the experimental data to date, concluding that the 0.2% disparity between the data and the predicted results is due to poorly known galactic constants, and that tighter bounds will be difficult to attain with current knowledge of these figures. They also mapped the pulsar's two-dimensional beam structure using the fact that the system's precession leads to varying pulse shapes. They found that the beam shape is latitudinally elongated, and pinched longitudinally near the centre, leading to an overall figure-of-eight shape.[3]

    From this i am trying to understand what is being converted into gravity waves, is it angular momentum, mass, or what.
    In a binary system how would one calculate which one would inspiral into the other.
    And how many watts per year for say a binary system of 1.5 solar masses each would be given off before coalition. given some arbitrary orbit.
     
  2. jcsd
  3. Jun 14, 2013 #2

    phyzguy

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    Misner,Thorne, and Wheeler (MTW) have a good derivation of the generation of gravitational waves by binary stars in chapter 36. For circular orbits, the power radiated in GW is given by:

    L(GW) = 32/5 μ^2 M^3 / a^5 where μ= m1*m2/(m1+m2) , M = m1+m2, and a is the radius of the orbit.

    For an elliptical obit, this gets multiplied by a complicated function of the eccentricity. Because most of the radiation is emitted near periastron, the GW radiation slowly circularizes the orbit. Also, because of the a^5 factor in the denominator, most of the energy is emitted just before coalescence. The gravitational waves carry off both energy (and thus mass) and angular momentum as the stars spiral in. I think in a typical NS/NS coalescence, the GW can carry off a significant fraction of a solar mass of energy.
     
  4. Jun 14, 2013 #3
    It is the rotational energy of the system (angular momentum and energy are not interchangeable) that is being carried away by the energy in the gravitational waves. Thus the decrease in the orbital period. Because of mass-energy equivalence, this loss of rotational energy would be measurable as a decrease in the mass of the binary system.

    Note, also, that the correct term is gravitational waves, not gravity waves. The distinction is important, because gravity waves are something else entirely, and unrelated to general relativity.
     
  5. Jun 15, 2013 #4

    Chalnoth

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    One could say it's gravitational potential energy. The system radiates, the two objects become closer together, meaning they have less gravitational potential energy (they also move faster, but the net is still a loss of energy).

    I'm sure whether or not the emitted radiation also has a net angular momentum. I would naively guess usually not, but it's certainly conceivable.
     
  6. Jun 15, 2013 #5

    phyzguy

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    I'm not sure either, but I think the gravitational waves must be carrying away angular momentum as well as energy. As the two stars spiral inward, the net angular momentum is decreasing. For two equal mass stars, I think the total angular momentum is proportional to sqrt(G*m^3*r). Where else can the angular momentum go except to be carried away by the gravitational waves?
     
  7. Jun 15, 2013 #6

    Chalnoth

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    Well, yes, if the angular momentum is decreasing, then certainly it must be carried away by the gravitational radiation.
     
  8. Jun 16, 2013 #7

    wolram

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    Thank you for the replys guys, you have cured my fuzzy head :biggrin:
     
  9. Feb 14, 2016 #8
    How does the gravity force formula apply now after the discovery of gravity waves?
     
  10. Feb 14, 2016 #9

    PeterDonis

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    What gravity force formula do you mean? Gravity is not a force in GR, and GR is the theory scientists use to analyze gravitational waves.
     
  11. Feb 14, 2016 #10

    Drakkith

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    It doesn't, just like Coulomb's law didn't change with the discovery of Electromagnetic waves.
     
  12. Apr 18, 2016 #11

    1oldman2

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