Comparison of two kinds of S-L coupling effects for binary pulsars

The orbital velocity of a binary pulsar system has been treated by different methods in pulsar timing measurement (former), and in the computation of the modulation of spin-orbit (S-L) coupling induced precession of orbital plane to gravitational wave (latter). From which the secular variabilities predicted are different significantly. This paper points out that reason for such differences is due to the different expressions to the S-L coupling effect by the two methods. This paper derives orbital velocity as well as secular variabilities through the method used in the latter case. It is likely that the secular variabilities obtained in the latter case can naturally explain corresponding observations, i.e., PSR 2051-0827, PSR 1957+20, PSR 1012+5307, and PSR 1713+0747