A New General Perturbation Method for Determining the Long-Term Motion of Comets

Abstract

A number of authors have used special perturbation methods to propagate Comet Halley back before its oldest observation in 239 BC. Unfortunately, results from these studies vary drastically because it is so difficult to accurately model nongraviatational forces acting on comets. In contrast, general perturbation methods do not need to model any forces and can be more accurate over long periods of time. Regrettably, the most recent general perturbation method used for Comet Halley introduced a lot of subjectivity. A new general perturbation method integrating Halley’s Comet back in time is presented here. This new method uses least squares, based solely on math. Therefore, it does not introduce any subjectivity. It also permits statistical analysis of the model’s accuracy. Using this model, Halley’s Comet is propagated back to 2317 BC, and with the derived equations it can easily be integrated back much further in time. Results are very similar to two previous studies by other authors, varying by less than five years when propagated back over 2,200 years. This same new general perturbation method is also applied to Comet Swift-Tuttle. Results with Swift-Tuttle compare reasonably well with the only other known research that integrated this comet back in time.