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

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

1998-10-19

arxiv.org/abs/physics/9810034v1

Eur. J. Phys. vol 19 (1998) 431-438

Physics

Classical Physics

9 pages, 4 figures

Scientific paper

10.1088/0143-0807/19/5/004

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.

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