Fast numerical approximation of invariant manifolds in the circular restricted three-body problem

• A method for fast evaluation of states defined on invariant manifolds in the circular restricted three-body problem is presented.
• The usefulness of the method for preliminary trajectory optimization is discussed.
• The developed methodology is assessed in terms of accuracy and computational efficiency.

In this paper a two-step approach to approximate the invariant manifolds in the circular restricted three-body problem is presented. The method consists in a two-dimensional interpolation, followed by a nonlinear correction. A two-dimensional cubic convolution interpolation is implemented to reduce the computational effort. A nonlinear correction is applied to enforce the energy level of the approximated state. The manifolds are parameterized by using two scalars. Results show efficiency and moderate accuracy. The present method fits the needs of trajectory optimization algorithms, where a great number of manifold insertion points have to be evaluated online.