The effect of gravitational radiation damping on the variation of the orbital elements of binary system is studied further base on our previous work[1].The result and correction for the previous paper are presented. The effect of gravitational damping on the time of passing perigee of binary star is given. The result shows clearly that the gravitational damping results in both the periodic and secular variation of the time of passing perigee, that is, the time of passing perigee moves up in every revolution. The numerical estimation for the effect on the variation of the time of passing perigee of binary stars, Y Cyg, PSR 1913+16 and PSR 2303+24 been made.
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