Overview

Basic to the determination of precision spacecraft orbits is an appropriate first approximation by a sequence of two-body orbits. For example, the initial portion of the orbit for a free-return, flyby, interplanetary voyage may be approximated by an ellipse whose focus is at the center of the sun. When the spacecraft is within the sphere of influence of the planet, the orbit is then essentially hyperbolic with the planet at the focus. Again for the return trip, the trajectory is approximated by an ellipse. For each of the three parts, the assumption is made that only one gravitational center is active at a time. The resulting orbit is an amazingly good representation of the actual motion and can be utilized for many important problems.

Although the patched-conic approximation, as it is frequently called, is not adequate as a precise reference orbit, it does afford a convenient means of exploring a variety of initial and boundary conditions at earth and the target planet in an efficient manner. Indeed, one can expect to achieve significant economies in computation time without compromising the essential ingredients of the problem.

When a precision orbit is obtained based on the conic approximations, certain quantities can be regarded as invariant: the total time of flight and the position vectors at the time of insertion into orbit and the return perigee are possible invariants. Thus, the approximate patched-conic solution can relate to the precise orbit in important and fundamental ways. Precision-orbit determination is accomplished by making...