The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

1. 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.
   
   
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. 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.
   
   
   
   
3. 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".
   

Below is a table with the orbital eccentricity of the eight planets and Pluto

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.

1.  Find the eccentricities of Neptune's and Pluto's orbits. Use the ellipse eccentricity animation to visualize the shape of the orbit of each planet.
Explain why the two orbits might intersect.

2.  The varying distance from the Earth to the Sun could potentially be why we have seasons, but in fact the seasons are due to the tilt of the Earth's rotation axis.  One reason it cannot be due to the ellipticity of Earth's orbit is that summer and winter do not occur at perihelion and aphelion.   Also Earth's orbit is too circular to produce much of an effect.  Can you think of a third reason why the seasons cannot be due to the changing Earth-Sun distance?

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.

3.  This question uses the above applet.   Turn on the "Elliptical Orbit" button, and trace the orbit of Mercury. Write down in the box below the ellipticity, and the distances from the Sun at perihelion and aphelion.  Now do the same for Venus.  How does ellipiticity relate to the variation between perihelion and aphelion distance?