The Great Martian Catastrophe and how Tycho (Re-)fixed it

Abstract

During Kepler’s time the ephemerides of the longitude of Mars were mainly calculated using the Alfonsine and the Prutenic tables. The error in the prediction of the longitudes was usually about 2 degrees for both, but in some critical situations, it could reach 5 degrees (in singular catastrophic events, as Owen Gingerich labeled them). Kepler’s Rudolphine tables diminish the error to just minutes of arc. Kepler introduced three novelties, all improving Mars’ predictions: 1) he made the orbits elliptical (first law), 2) he replaced the equant point by the area law (second law), and, finally 3) he bisected the orbit of the Earth. James Voelkel and Gingerich analyzed the degree of responsibility that each of Kepler’s novelties has in the improvement of the predictions of Mars’ longitude and suggest that while around 0.5 degree of the error is solved introducing the first two laws, the remaining around 4.5 degrees disappear once you introduce the bisection of the orbit of the Earth. In this paper I will argue that the distribution of the responsibility is actually different: while 0.5 degree must be attributed to the first two laws, only another 0.5 must be attributed to the bisection of the eccentricity of the Earth, and the remaining around 4 degrees are due to an error in the longitude of the apogee. There is evidence that Tycho and Longomontanus had a correct value of the longitude of the apogee before Kepler’s arrival to work with them in Prague. Therefore, it was Tycho and not Kepler who solved the main part of the catastrophe of Mars, even if not the most difficult one.