Abstract: The restricted three-body problem is a Hamiltonian dynamical model used usually in dynamics of the solar system. At present, Numerical methods are mainly adopted for some important problems. It is due to the fact that the mathematical tools or methods are poor. But, in order to understand the evolution of the solar system, it needs to dolong-term tracking computations. Hence the requirement for algorithms is very high, that is to say, the algorithms must maintain the global characteristics of the motions. The symplectic algorithms just satisfy the requirement. In this paper, an explicit symplectic difference scheme has been constructed for circular and elliptic restricted three——body problem in the rotative coordinate system by means of algorithm composition, respectively.Some computational examples have shown the scheme is effective.

Key words: restricted three-body problem, Hamiltonian system, symplectic algorithm, algorithm composition, symplectic structure