The Greeks regarded the heavens as the epitome of perfection. All flaws and blemishes were confined to the terrestrial domain. Since the circle is perfect in its infinite symmetry, it was concluded by Aristotle that the Sun and planets move in circles around the Earth. Later, the astronomer Ptolemy accounted for deviations by means of additional circles, or epicycles. He stuck with the circular model [TM162 or search for “thatsmaths” at irishtimes.com].
Left: Elliptic orbit with velocity vectors. Right: Hodograph, with all velocity vectors plotted from a single point.
Continue reading ‘Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph’
