Compact analytic solutions for a decaying, precessing circular orbit

The evolution of low Earth orbit satellites under the action of atmospheric drag and J2 oblateness perturbations has been widely investigated. Simple analyses describing the altitude decay of a circular orbit through energy arguments have also been widely available. This paper extends these simple analyses by providing compact analytic expressions for true anomaly and ascending node angle along with a more accurate expression for altitude decay. The resulting solutions then allow a fast and efficient method of investigating the orbital evolution of decaying, precessing circular orbits. Applications include the rapid evaluation of station-keeping budgets for both single platforms and the orbital evolution of satellite constellations. Passive station-keeping by continuous low thrust acceleration is investigated and shown to be naturally unstable.