A noncanonical analytic solution to the J2 perturbed two-body problem

The motion of a satellite subject to an inverse-square gravitational force of attraction and a perturbation due to the earth's oblateness as the J2 term is analyzed, and a uniform, analytic solution correct to first-order in J2, is obtained using a noncanonical approach. The basis for the solution is the transformation and uncoupling of the differential equations for the model. The resulting solution is expressed in terms of elementary functions of the independent variable (the 'true anomaly'), and is of a compact and simple form. Numerical results are comparable to existing solutions.