Perturbation of Uranus by Neptune: A modern perspective

The perturbation of Uranus by Neptune is analyzed in a simple model, in which the unperturbed orbits are regarded as circular and coplanar. Both the forward problem of calculating the deviation in the position of Uranus and the inverse problem of using the observed deviations to infer the elements of Neptune are attempted. The model accounts for the data quite well, offering a simple understanding of its features. Because the perturbation is nearly resonant, the effect of Neptune is actually an order of magnitude larger than the historically reported remaining deviation and the inverse problem also admits a fairly good solution that places Neptune in a diametrically opposite position.