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As is well known, Johannes Kepler (1571-1630) was the first astronomer to correctly describe the motion of the planets
(in works published between 1609 and 1619). This motion is summed up
in three simple laws:
Let us now see if we can derive Kepler's laws from Equation (4.2).
- The planetary orbits are all ellipses that are confocal with the Sun
(i.e., the Sun lies at one of the focii of each ellipse--see Section A.9).
- The radius vector connecting each planet to the Sun sweeps out equal areas in equal time intervals.
- The square of the orbital period of each planet is proportional to
the cube of its orbital major radii.