| Kepler's
equant law suggests that if a planet sweeps out equal angles in
equal times with respect to the kenofocus (empty focus F), it will pass
through arcs AB and CD in equals times, since angles alpha and beta are
equal. Hence a given planet moves faster along arc AB (perihelion) than
arc CD (aphelion). However, Kepler's vicarious hypothesis required a circular
orbit rather than an ellipse. Kepler's vicarious hypothesis employed eccentric
motion without employing Ptolemy's famous bi-section of the eccentricity.
Such a construction results in errors of about 7.5' at the octants of the
planetary path. |
