























































KEPLER'S 1^{st} LAW
The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. 
















































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 we call ellipses. 
















THE BASIC PROPERTIES OF ELLIPSES
 For an ellipse there are two points called foci (the singular is focus) such that the sum of the distances to the foci from any point on the ellipse is a constant. In terms of the diagram above, with "the black X" marking the location of the foci, we have the equation: x+y=constant that defines the ellipse in terms of the distances x and y.
 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. As the ellipse becomes more flattened the eccentricity approaches one. Thus, all ellipses have eccentricities lying between zero and one. The orbits of the planets are ellipses but the eccentricities are so small, for most of the planets, that they look circular at first glance.
One must measure the geometry carefully to determine that their orbits are not circles, but ellipses of small eccentricity. Pluto and Mercury are exceptions: their orbits are sufficiently eccentric to see that they are not circles.
 The long axis of the ellipse is called the major axis, while the short axis is called the minor axis. Half of the major axis is termed the semimajor axis. The length of the semimajor axis is often termed the radius of the ellipse. It can be shown that the average separation of a planet from the Sun as it goes around its elliptical orbit is equal to the length of the semimajor axis. Thus, by the "radius" of a planet's orbit one usually means the length of the semimajor axis.
The semimajor axis is typically labeled
"a".





















Click Here
to view the various eccentricities from 0 to 0.9.
Below is a table with the orbital eccentricity of the
eight planets and Pluto 













BODY

ECCENTRICITY

Mercury

0.206

Venus

0.007

Earth

0.017

Mars

0.093

Jupiter

0.048

Saturn

0.056

Uranus

0.047

Neptune

0.009

Pluto

0.249












Notice that the
Earth's orbit is only slightly elliptical. You might think
the Earth's varying distance from the Sun is responsible for
the seasons. But this effect is very small. The seasons
are due to the Earth being tilted on its axis.
Try this applet to
trace out the actual orbits of the planets, as well as Pluto
and Halley's Comet. Scroll down to the applet, turn on
"Elliptical orbit", "Axes", and "Connecting Lines", choose
an object, and drag it around its orbit with the mouse. Note
the shape, the value of the ellipticity, and the position of
the Sun. 


