The solution to the three-body problem and some applications (Q2420839)

The solution of the three-body problem is presented in the context of solving the Sun-Earth-Moon dynamic system problem. The orbit and the vibrations of the orbital parameters of the Moon are described by means of simple periodic functions. The internal Hamiltonian and the Lagrange equations have been applied to computations. The article presents a new set of weighted colour coordinates YJK in the colour space. It also explains the coordinate transformation between the absolute Cartesian coordinates, relative coordinates and centre-of-mass coordinates in terms of weighted quadratic forms. The provided calculations fully explain the main problem of the lunar theory. The results are consistent with experimental data but different from the analysis based on the method of normal modes of vibration. The introduction of missed terms into the Hamiltonians can provide faster and better computations.