We discuss the use of dimensional analysis and the quadrupolar emission hypothesis to determine the gravitational power radiated by a celestial body in a circular orbit. We then show how to derive the instantaneous power radiated in a general Keplerian orbit by approximating it locally by a circle. This derivation allows us to recover with good accuracy the nontrivial dependence given by general relativity relating the average radiated power to the eccentricity of an ellipse. The approach is understandable by undergraduate students.
REFERENCES
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A different discussion of the gravitational power is given in
Bernard F.
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(Cambridge U. P.
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, 2003
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.9.
If we had taken instead of in the equality, the constant would have been multiplied by a very large factor , and the dimensional analysis would not have yielded the right order of magnitude. The choice of instead of for the characteristic time of evolution of harmonic phenomena is discussed for example in
Jean-Marc
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and Françoise
Balibar
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, Amsterdam
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This dependence on is commonly associated in physics courses with Rayleigh scattering and the blue color of the sky.
11.
The equation for the orbit of the reduced mass is , with . The magnitude of the acceleration is .
12.
See, for example,
L. D.
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For charges involved in harmonic motions ( fixed) on elliptical trajectories, is proportional to , where ; then is a reducing factor.
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2009
American Association of Physics Teachers
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