Computation of orbits using total energy

The computation of orbits can be done more efficiently by the use of any of several new formulations of the perturbed two body problem which consider the total energy of the orbital system as one of the dependent variables. The total energy is the osculating two body energy plus the potential energy due to perturbing masses. The use of the total energy as the dependent variable instead of the two body energy is a relatively new idea. The advantage of using total energy arises from the fact that the more perturbing potential energy that is accounted for in the total energy variable, the more nearly constant is the total energy. In fact, except for dissipative forces such as drag, the only reason for the total energy not being constant is the rotation or revolution of the perturbing mass. This near constancy of the total energy has the effect of inhibiting error growth during numerical solution. This paper will present the results of an application of total energy formulation to the problem of the precise computation of orbits.