## A series solution for some periodic orbits in the restricted three-body problem according to the perturbation method |

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Aeronautics and Space artificial satellites asteroid belt asteroids avoid places avoid certain areas Celestial Mechanics D-2488 National Aeronautics derived developed and numerically direct integration dust particles earth Earth-Moon system eigen value Equation 46 Equation 51 Equations 15 expansion given by Equations Huang Goddard Space initial conditions predicted initial values integration constants Kirkwood gaps kn and ln less massive finite massive finite body METHOD by Su-Shu moon NASA NASA TN NASA TECHNICAL NOTE nearly periodic orbits neighborhood numerically verified obtained by purely orbit is developed orbits are compared orders of approximation OTS price particles may avoid period of Jupiter periodic solution PERTURBATION METHOD perturbation theory purely numerical processes quantum mechanics restricted three-body problem satellites and dust series is obtained SERIES SOLUTION simple theory Space Administration Su-Shu Huang Goddard synchronous orbit Szebehely TECHNICAL NOTE D-2488 theory of nearly THREE-BODY PROBLEM ACCORDING TN D-2488 commeasurable TN D-2488 National verified by examples