Abstract: Angular momentum conservation, a fundamental principle in classical mechanics and astrophysics arising from the rotational symmetry of space, plays a decisive role in the evolution of close binary systems. Focusing on angular momentum conservation, this paper systematically analyzes the evolutionary patterns of orbital periods in binary systems undergoing mass transfer. By constructing an idealized binary orbital model, we derive the quantitative relationship between the rate of orbital period change and both the mass ratio and the direction of mass transfer, under the assumptions of total mass conservation and the absence of external torques. The study finds that when the less massive star steadily transfers matter to its more massive companion, the orbit expands and the orbital period increases. Conversely, mass transfer in the opposite direction leads to orbital shrinkage and a period decrease; however, such a process is often accompanied by thermodynamic instabilities, making it difficult to sustain over long timescales. Our theoretical predictions are further validated by observational data from the eclipsing binary system J101330.8+494846. We also note that in realistic systems, mechanisms such as magnetic braking, gravitational radiation, or mass loss often result in angular momentum loss, leading to a continuous orbital decay. This work not only deepens the understanding of the physical implications of angular momentum conservation but also provides students with a bridge connecting fundamental physical principles to cuttingedge astrophysical research, offering significant pedagogical and heuristic value for scientific initiation.

Key words: angular momentum conservation, mass transfer, orbital period evolution, close binaries, angular momentum loss, integration of education and research