The N-body problem is defined and its equations of motion are presented. Anew time transformation based on two-body problem series solutions is introducedand used to develop a time-dependent, analytic, first-order solution ofthe N-body problem. A process of deriving higher-order, time-dependent, analyticsolutions of the N-body problem is also introduced. These analytic solutionsare used to investigate periodic and non-periodic trajectories in the restrictedthree-body problem and are shown to be capable of describing complete,N-body trajectories with good accuracy and with far fewer function evaluationsthan are required by numerical integration.
展开▼
