We study the pseudo-synchronous orbital motion of a binary system on the main sequence. The equations of the pseudo-synchronous orbit are derived up to O(e4) where e is the eccentricy of the orbit. We integrate the equations to present their solutions. The theoretical results are applied to the evolution of the orbit and spin of the binary star Y Cygni, which has a current eccentricity of e0 = 0.142. We tabulate our numerical results for the evolution of the orbit and spin per century. The numerical results for the semi-major axes and rotational angular velocities in the evolutional time scales of three stages (synchronization, circularization, and collapse time scale) are also tabulated. Synchronization is achieved in about 5 × 103 years followed by circularization lasting about 1 × 105 years before decaying in 2 × 105 years.

Abstract
1. INTRODUCTION
2. DEFINITION OF PSEUDO-SYNCHRONIZATION
3. PSEUDO-SYNCHRONOUS EQUATIONS AND THEIRSOLUTIONS
4. PSEUDO-SYNCHRONIZATION OF ORBIT AND SPININ Y CYGNI
5. CONCLUSION
REFERENCES

• Lin-Sen Li(School of Physics, Northeast Normal University) Corresponding author