Some notes on applying the one-step multiconic method of trajectory propagation

The one-step multiconic method (also called the pseudostate method) has been known for years to offer up to an order of magnitude of improvement over the patched-conic method for propagating trajectories under the gravitational influence of two bodies. In these notes, the method and some of its variations are described. Then, a crucial parameter of this method, the sweepback duration, is examined, and it is shown that the traditional wisdom concerning this parameter should be replaced by an algorithm which relates it to the trajectory characteristics. Remarkably, this algorithm is independent of the masses of the primary and secondary bodies.