Abstract A set of synchronous equations are derived from a set of non-synchronous equations. The analytical solutions are given by solving the set of differential equations. The results of the evolutionary trend of the spin-orbit interaction are that the semi-major axis gradually shrinks with time; the orbital eccentricity gradually decreases with time until orbital circularization occurs; the orbital period gradually shortens with time and the rotational angular velocity of the primary component gradually speeds up with time before the orbit achieves circularization. The theoretical results are applied to evolution of the orbit and spin of synchronous binary stars Algol A and B that are on the main sequence. The circularization time, lifetime and the evolutionary numerical solutions of orbit and spin when circularization time occurs are estimated for Algol A and B.
Keywords binaries: close — rotation — evolution
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