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We examine the equant model for the motion of planets, which has been thestarting point of Kepler's investigations before he modified it because of Marsobservations. We show that, up to first order in eccentricity, this modelimplies for each orbit a velocity which satisfies Kepler's second law andHamilton's hodograph, and a centripetal acceleration with an inverse squaredependence on the distance to the sun. If this dependence is assumed to beuniversal, Kepler's third law follows immediately. This elementary execice inkinematics for undergraduates emphasizes the proximity of the equant modelcoming from Ancient Greece with our present knowledge. It adds to itshistorical interest a didactical relevance concerning, in particular, thediscussion of the Aristotelian or Newtonian conception of motion.

Had the planet mars not existed: Kepler's equant model and its physical consequences