Longomontanus’ Model for the Longitudes of Mars

Abstract

When at the beginning of 1600, Kepler arrived to work with Tycho Brahe, Longomontanus, Tycho’s principal assistant, who was working with a model for Mars that predicted with remarkable accuracy its longitudes at oppositions. According to Kepler, this hypothesis “represented all these oppositions within a distance of two minutes in longitude.” The model, however, was unsuccessful in predicting longitudes at other elongations from the Sun, and latitudes even at opposition. Much has been said on how Kepler developed his model after this meeting, arriving finally at the so-called first two laws published in his Astronomia Nova in 1609. By contrast, Longomontanus’ attempt, published as a final model in his Astronomia Danica, has received little scholarly attention. In this paper, I will systematically analyse and explain this model. Even if Longomontanus’ solution is not as elegant as Kepler’s, it deserves scholarly attention, both because it solves the problems posed by the model that he and Tycho were working on when Kepler arrived and because it offers an interesting though heterodox solution that, by contrast, helps to highlight the elegance and simplicity of Kepler’s own solution.