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The sets of the synchronous equations are derived from the sets ofnon-synchronous equations The analytical solutions are given by solving the setof differential equations. The results of the evolutionary tendency of theorbit-spin are that the semi-major axis shrinks gradually with time: theorbital eccentricity dereacses gradually with time until the orbitalcircularization; the orbital period shortens gradually with time and therotational angular velocity of primary component speed up with time graduallybefore the orbit-rotation achieved the circularization The theoretical resultsare applied to evolution of the orbit and spin of synchronous binary starsAlgol A, B on the main sequence phase The circularization time and life time(age) and the evolutional numerical solutions of orbit and spin whencircularization time are estimeted for Algol A, B. The results are discussedand concluded.

Orbit and spin evolution of the synchronous binary stars on the main sequence phase