Seminar Review: Is the Solar System Stable? - Revisiting a Historical Topic

On November 15, Professor Jintai Ding, Dean of the School of Mathematics and Physics at Xi'an Jiaotong-Liverpool University, invited Professor Chongqing Cheng from Nanjing University to deliver a fascinating lecture titled "Is the Solar System Stable? - Revisiting a Historical Topic" for our faculty and students. Professor Cheng delved into the dynamical stability of the solar system, a topic with a long history and central importance in celestial mechanics.

Professor Jintai Ding

The lecture began with an introduction to Kepler's laws and Newton's law of universal gravitation, where Professor Cheng detailed how these laws are used to prove the correctness of Kepler's laws and discussed the characteristics of the solar system as a perturbed two-body system. He then reviewed the fundamental scientific questions of the 18th century regarding the stability of the solar system, particularly the impact of mutual perturbations among planets on the system's stability.

 Professor Chongqing Cheng

During the lecture, Professor Cheng also introduced the work of Lagrange, Laplace, and Poisson, who proved the long-term invariance of the semi-major axes of planetary orbits. Furthermore, Professor Cheng discussed the variational principle, Lagrange's equations, and Hamilton's equations, along with their applications in describing celestial motion.

Professor Cheng's lecture covered not only theoretical aspects but also practical applications, such as the Kolmogorov-Arnold-Moser (KAM) theorem in Hill's lunar theory, the motion of charged particles in magnetic fields, fluid dynamics, and the discovery and application in the Van Allen belts around the Earth.

At the end of the lecture, Professor Cheng explored the long-term stability of the solar system, emphasising that while the KAM theorem provides theoretical support for the short-term stability of the solar system, its explanation for long-term stability remains limited, and the Arnold diffusion phenomenon is significant for understanding the dynamic changes in the solar system.

Professor Chongqing Cheng is the chairman of the Jiangsu Mathematical Society and an expert in the mathematical academic degrees committee of the State Council discipline appraisal group. His main research field is dynamical systems. He received the Second Prize of the National Natural Science Award in 2001 (as the first completer) and was invited to give a report at the International Congress of Mathematicians in 2010.

By Qinru Liu