It fell to Kepler to provide the final piece of the puzzle: after a long
struggle, in which he tried mightily to avoid his eventual conclusion,
Kepler was forced finally to the realization that the orbits of the
planets were not the circles demanded by Aristotle and assumed
implicitly by Copernicus, but were instead the "flattened circles" that
geometers call ellipses. This was achieved by Kepler's work on
all the Mars observations given him by Tycho Brahe, and Mars just happened
to be the most un-circular orbit of all planets then known!
Properties of Ellipses
1. An ellipse has two foci. The sum of the distances to the foci from
any point on the ellipse is a constant (A + B = Constant). A circle is
a special type of ellipse, where A = B.
2. The amount of "flattening" of the ellipse is termed the eccentricity.
A circle may be viewed as a special case of an ellipse with zero eccentricity.
Typical eccentricity of the planets is a few percent (nearly circular!).
3. The long axis of the ellipse is called the major axis, while the short axis is called the minor axis (adjacent figure). Half of the major axis is termed a semimajor axis. The length of a semimajor axis is often termed the size of the ellipse. With planets, the semi-major axis refers to the orbital distance.
Kepler's First Law:
I. The orbits of the planets are ellipses, with the Sun at one focus of
the ellipse. |
![]() |