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The hodograph, i.e. the path traced by a body in velocity space, wasintroduced by Hamilton in 1846 as an alternative for studying certain dynamicalproblems. The hodograph of the Kepler problem was then investigated and shownto be a circle, it was next used to investigate some other properties of themotion. We here propose a new method for tracing the hodograph and thecorresponding configuration space orbit in Kepler's problem starting from theinitial conditions given and trying to use no more than the methods ofsynthetic geometry in a sort of Newtonian approach. All of our geometricconstructions require straight edge and compass only.Comment: 9 pages, 4 figure

From circular paths to elliptic orbits: a geometric approach to Kepler's motion