
Measuring eccentricity: Eccentricity of your ellipse is measured by comparing two lengths on the ellipse: the major axis and minor axis.
A circle is an ellipse where the major axis = the minor axis (they're the same length). In addition, the foci appear on top of each other (there would only be one dot in the center instead of two dots spread apart). As the major axis gets longer than the minor axis, the eccentricity of the ellipse increases. The eccentricity involves a ratio of the two axes. An ellipse with an eccentricity of 0.00 (no difference between axis lengths) is a perfect circle. An ellipse with an eccentricity of nearly 1.00 is an extremely squashed oval. Remember, the major axis must be equal to or larger than the minor axis, and neither number should be zero! Study the diagram above, and when you feel confident with the anatomy of your ellipse, take the following measurements (in either feet, inches, centimeters, or millimeters): the length of the major axis the length of the minor axis Now that you have these measurements, put them into the following boxes, and your ellipse's eccentricity will be determined for you! No conversions between units are needed, since the math in this calculation only involves ratios. Click on the zeros to enter in your two values and make sure to press enter / return on the keyboard. Unfortunately this will not work if your computer doesn't have Microsoft Excel.
If you are interested in trying the math on your own, here is the full equation (a = major axis, b = minor axis):
As you can see, both the major and minor axes are halved. This equation uses what are called the semimajor axis (^{a}/_{2}) and the semiminor axis (^{b}/_{2}). A calculator might be useful in computing eccentricity on your own (make sure you use parentheses). The volunteers can also show you this step with the calculator we have at the observatory. Technically, there is another way to compute the eccentricity of an ellipse with easier math, but it requires more complicated measurements. To see this method, go to the next page.


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