Newton and celestial mechanics
Newton's achievements in celestial mechanics tend in popular accounts to be underestimated in some respects, exaggerated in others. This chapter seeks to correct a number of misconceptions arising from inattention to the detailed history.
The claim that the planets move in elliptical orbits, with the radii vectores from Sun to planet sweeping out equal areas in equal times, first appeared in Kepler's Astronomia Nova of 1609. Since the late eighteenth century the two parts of this claim have been referred to as Kepler's first two planetary “laws, ” understood as empirical laws. According to the popular account, Newton relied on these “laws” as thus established.
Writing to Halley on 20 June 1686, Newton stated: “Kepler knew ye Orb to be not circular but oval & guest it to be elliptical. ” 1 Whether Newton ever saw the Astronomia Nova is unknown.
The Astronomia Nova is an innovative work. It establishes important empirical results, such as the passage of the planet's orbital plane through the Sun's center and the orbit's oval shape. Was the orbit's ellipticity also a straightforwardly empirical result, say by means of triangulations of Mars, as sometimes asserted? 2 Kepler carried out many such triangulations, but they were subject to sizeable observational error, of which he was acutely aware. 3
At the end of Chapter 58 we at last find him asserting that “no figure is left for the planetary orbit but a perfect ellipse. ” This chapter attempts to refute another oval orbit, the via buccosa or puffycheeked path. Kepler's whole effort, he tells us, has been to find a