Vector kinematic analysis of Keplerian velocity from Hamilton’s hodograph

Abstract Many authors in literature have focused on Hamilton’s hodograph of the Keplerian motion, but none of them developed a vector kinematic analysis of the peculiar velocity shown by the hodograph, so we perform it here. This approach gives a new interpretation of gravitation, revealing that it causes rotation but not attraction, together with an alternative way to teach and learn the Keplerian motion, easier to handle than the classical one based only on Newton’s gravitational force. As expected, the analysis predicts the mathematical structure of Newton’s acceleration and Kepler’s laws, however a kinematic factor replaces Newton’s physical factor GM. It also leads to new expressions for the eccentricity and the classical mechanical energy, as well as a new interpretation of bodies falling and a new solution to explain the rotation of spiral galaxies