SYMPLECTIC INTEGRATORS FOR LONG-TERM INTEGRATIONS IN CELESTIAL MECHANICS

We discuss the use of symplectic integration algorithms in long-term integrations in the field of celestial mechanics. The methods' advantages and disadvantages ( with respect to more common integration methods) are discussed. The numerical performance of the algorithms is evaluated using the 2-body and circular restricted 3-body problems. Symplectic integration methods have the advantages of linear phase error growth in the 2-body problem ( unlike most other methods), good conservation of the integrals of the motion, good performance for moderately eccentric orbits, and ease of use. Its disadvantages include a relatively large number of force evaluations and an inability to continuously vary the step size.