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Posted by Alexander on March 20, 2001 00:50:16 UTC

In weak gravitational radiation orbit in 1/r potentials is (in polar coordinates) the solution of the Newton's equation m(d2r/dt2)=-GM1M2/r, and this solution is r(alpha)=se/(1-ecos(alpha)), where e is excentricity (e depends on initial velocity, and results in parabola if e=1, ellipse if e1, circle if e=0), s - is size (scale) of orbit.

In strong gravitational field gravitational radiation will carry away energy, and instead of ellipse, for example, you will get set of spiraling curves resembling ellipses. You can get them by introducing non-zero gravitational "friction" term dr/dt in the above equation. For small friction you still get ellipses with Sun in one focus, but they will presess (turn), for strong gravitational radiation - more fancy and steep spirals.

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