In the Introduction Gauss made the standard laudatory remarks about Newton’s genius and Newtonian mechanics. After paying his respect to Newton Gauss ignored him. In the astronomical part of the book Gauss used only trigonometric formulas and Kepler’s rule. Nothing discovered by Newton was used to predict the orbit of Ceres.
Newton himself invented this method of using trigonometric algorithms and then attributing the results to Newtonian universal law of gravitation. Newton conspired with Halley and stole Astronomer Royal’s observations and had Halley compute the orbit of the comet from this trigonometric curve fitting method explained in Principia Book 3, Proposition 41. To this day, the prediction of the Halley’s comet’s return is given as a proof of Newton’s laws.
Prior to Newton, Cassini, Borelli, Dorfell, Wren, Hooke and Horrocks all suggested parabolic and elliptic paths for comets. In III.41 Newton sketched a geometric method of deriving the orbits of comets from observations and using this method Halley computed parabolic orbits of 24 comets of which two had appeared in 1337 and in 1427 and the others in the sixteenth and seventeenth centuries.
These geometric computations suggested to Halley that three of them had nearly identical orbits. Since both intervals were 76 or 75 years, he concluded that they were three successive appearances of the same comet. No Newtonian notions of universal gravity were used to predict the return of any comet. ((The story of this dynamic duo of scientific fraud is told in Newton’s Tyranny: The Suppressed Scientific Discoveries of Stephen Gray and John Flamsteed)) Newtonian propaganda has been presenting this as yet another vindication of Newton’s grand theory of gravitation. Why do physics teachers still teach this Newtonian propaganda as historical truth to students?