  We examine the equant model for the motion of planets, which has been the
starting point of Kepler's investigations before he modified it because of Mars
observations. We show that, up to first order in eccentricity, this model
implies for each orbit a velocity which satisfies Kepler's second law and
Hamilton's hodograph, and a centripetal acceleration with an inverse square
dependence on the distance to the sun. If this dependence is assumed to be
universal, Kepler's third law follows immediately. This elementary execice in
kinematics for undergraduates emphasizes the proximity of the equant model
coming from Ancient Greece with our present knowledge. It adds to its
historical interest a didactical relevance concerning, in particular, the
discussion of the Aristotelian or Newtonian conception of motion.
