In the classical mechanics, the problem of many body gravitation has always been a hot topic.But in addition to the early two-body gravity problem, three-body and more than three-body can not provide analytical solutions.Because in three-dimensional space, only 10 algebraic equations can be obtained after the vector is decomposed(Three equations can be obtained from centroid,three equations can be obtained from the law of conservation of momentum,three equations can be obtained from the law of conservation of angular momentum,and the last can be obtained from the law of conservation of energy).We can't get enough algebraic equations to relate the differential equations of three-body motion problems,so it can't be solved accurately.But not all cases are unsolved. By simplifying some conditions, we can still get the analytical solution of some three-body problems, which are called restricted three-body problems.In this paper, a theorem is introduced and proved, which can provide a new way to solve the solvable condition of restricted three body problem.