The field of Celestial Mechanics, relating the complexity of the calculation of planetary movements with different interactive forces, historically started with the study of the two-body problem. Since then, the study of the (n+1)-body problem has been an important part of the Celestial mechanics. The study of the movement of three bodies under mutual gravitational forces was first attempted by Sir Isaac Newton in his ground-breaking work “Principia”. However, the problem remained unsolved for n≥2. These problems were made more approachable by Forest Ray Moulton in 1917 by introducing the concept of “Restricted three body problem” in his book “An introduction to Celestial Mechanics”.

In the restricted problem, one of the participating bodies is assumed to be of negligible mass, thereby not contributing to the perturbing forces affecting the movement of other bodies. The restricted three-body problem (both circular and elliptical) was explored extensively by many mathematicians and physicists during the 19th and 20th century. The problem has undergone extensive treatment both in terms of analytical and numerical tools. Inspired by the restricted three-body problem, the study of the four-body problem was also simplified by firstly considering one of the bodies to be of negligible mass and position of the other three bodies according to different configurations such as equilateral triangular configuration or bicircular formation. In these studies, it has been found that not only gravitational forces but also many other perturbing forces influence the dynamics of the problem.

The aim of this Special Issue is to collate original research and review articles that focus on the entire range of the restricted (n+1)-body problem, where n≥2. This issue will include both observational and theoretical research articles and data analysis related to planetary movements. The techniques employed for theoretical study may be analytic, semi-analytic, or numerical.

Potential topics include but are not limited to the following:

• Perturbed restricted (n+1)-body problems (n≥2) (especially 3, 4, or 5-body problems)
• Perturbation methods
• Analytical and semi-analysis methods for relative motion and periodic orbits
• Stability analysis
• Other orbital dynamics
• New analytical or computational methods applicable to the problem