Hodographs for the Kepler problem are circles. This fact, known for almost two centuries, still
provides the simplest path to derive the Kepler first law. Through Feynman?s ?lost lecture?, this
derivation has now reached a wider audience. Here we look again at Feynman?s approach to this
problem, as well as the recently suggested modification by van Haandel and Heckman (vHH), with two
aims in mind, both of which extend the scope of the approach. First we review the geometric
constructions of the Feynman and vHH approaches (that prove the existence of elliptic orbits without
making use of integral calculus or differential equations) and then extend the geometric approach to
also cover the hyperbolic orbits (corresponding to ##IMG##
[http://ej.iop.org/images/0143-0807/37/2/025004/ejpaa12c9ieqn1.gif] {$Egt 0$} ). In the second part
we analyse the properties of the director circles of the conics, which are used to simplify the
approach, and we rela…