Some Properties of Ellipses

# Some Properties of Ellipses - the planets that they look...

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Some Properties of Ellipses Since the orbits of the planets are ellipses, let us review a few basic properties of ellipses. 1. For an ellipse there are two points called foci (singular: 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 shown to the left, with "x" marking the location of the foci, we have the equation a + b = constant that defines the ellipse in terms of the distances a and b . 2. The amount of "flattening" of the ellipse is termed the eccentricity . Thus, in the following figure the ellipses become more eccentric from left to right. A circle may be viewed as a special case of an ellipse with zero eccentricity, while 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
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Unformatted text preview: the planets that they look circular at first glance. For most of the planets one must measure the geometry carefully to determine that they are not circles, but ellipses of small eccentricity. Pluto and Mercury are exceptions: their orbits are sufficiently eccentric that they can be seen by inspection to not be circles. 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. 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. For a more detailed investigation of the properties of ellipses, see this java applet...
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