Tracing a planet's orbit with a straight hedge and a compass with the help of the hodograph and the Hamilton vector

We describe a geometrical method for tracing a planet's orbit using its velocity hodograph, that is, the path of the planet's velocity. The method requires only a straight edge, a compass, and the help of the hodograph. We also obtain analitically the hodograph and some of the features of the motion that can be obtained from it.