Abstract This paper provides a method to study the solution of equations for synchronous binary stars with large eccentricity on the main sequence. The theoretical results show that the evolution of the eccentricity is linear with time or follows an exponential form, and the semi-major axis and spin vary with time in an exponential form that are different from the results given in a previous paper. The improved method is applicable in both cases of large eccentricity and small eccentricity. In addition, the number of terms in the expansion of a series with small eccentricity is very long due to the series converging slowly. The advantage of this method is that it is applicable to cases with large eccentricity due to the series converging quickly. This paper chooses the synchronous binary star V1143 Cyg that is on the main sequence and has a large eccentricity (e = 0.54) as an example calculation and gives the numerical results. Lastly, the evolutionary tendency including the evolution of orbit and spin, the time for the speed up of spin, the circularization time, the orbital collapse time and the life time are given in the discussion and conclusion. The results shown in this paper are an improvement on those from the previous paper.
Keywords binaries: close — rotation — evolution
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