Kepler's third law of n-body periodic orbits in a Newtonian gravitation field

• 来源期刊: 中国科学:物理学 力学 天文学（英文版）
• 年，卷（期）: 2018,（5）
• 页码范围: 65-68
• 页数: 4页
• 语种: 英文

摘要

One of the central and most vivid problems of celestial mechanics in the 18th and 19th centuries was the motion description of the Sun-Earth-Moon system under the Newtonian gravitation field (Figure 1 (a)).Notable work was done by Euler (1760),Lagrange (1776),Laplace (1799),Hamilton (1834),Liouville (1836),Jacobi (1843),and Poincaré (1889)[1] and Xia (1992) [2].The study of the motion between the two bodies was solved by Kepler (1609) and Newton (1687)early in the 17th century.For the elliptic periodic orbit of 2-body system,Kepler's third law of the two-body system [3] is given by T|E|3/2 =π/√2Gm1m2 √(m1m2)/(m1+m2),where the gravitation constant,G =6.673 × 10-11m3 kg-1 s-2,the orbit period,T,the total energy of the 2-body system,|E|,and point masses m1 and m2 (Figure 1(b)).