Some Simple Results Regarding Gravitational Disturbance by Exterior Planets--with Historical Applications

Abstract

Because of the present apparent difficulties with Neptune's motion, Brown's transformation of the longitudinal perturbation problem is revived and past papers on the subject are criticized. The awkward behaviour of the traditional perturbation function is remarked, for purposes of contrast, but then is examined in relation to the disturbed elements and thereby shown to represent no physical difficulty, thus incidentally invalidating Peirce's case against the Adams–Leverrier discovery of the planet Neptune. Coefficients and curves of transformed perturbations are provided for circular orbits, and a few possible applications and implications are considered. Among other results, the true relation of longitudinal perturbation-strength to distance is finally discovered.