Perturbation theory studies the effect of small parameters on a given equation. Applied to orbital mechanics, these minute changes can be measured and used to detect changes in periodic phenomena. One such periodic phenomena is the time of arrival (TOA) of regularly detectable pulses from a pulsar, a rapidly rotating star. Perturbations can be modeled theoretically and then matched with experimental data in order to discern if it is likely that a given planet-pulsar system has an exomoon. The original mathematical analysis of this phenomenon was conducted out to order O(ε²) and found that, for the case of a theoretical Jupiter-Jupiter system, a perturbation of 960 ns would occur. Our analysis expands the Maclaurin Series of the perturbed problem to order O(ε³) and for the same system determines an additional perturbation of 46 ns, indicating an improved threshold for detectability of the exomoon. Computational software was also used to explore a general form for the terms of order ε⁴ and higher to explore the limits of a useful approximation.