Periodic motions of a planetary system with double planets. Generalized Hill problem (Q1596158)

The author discusses the problem on motion on the Euclidean plane of a system of \(N+1\) material points which are attracted to each other by the Newton law. It is assumed that the Sun is the central body of the system with mass \(\,m_0=1\,\) while the masses \(m_i\) of the other bodies (planets) are small and their sum is a small parameter of the problem. The author describes the \(N\)-parametric family of unperturbed motions of the system and determines the family of \(T\)-periodic motions in the rotating system of coordinates with constant angular velocity.