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Ellipses

Ellipses. Ellipse. An ellipse is a closed curve around two fixed points called foci . Earth, and all the planets, revolve around (orbit) the sun in an eccentric, elliptical orbit; However, the distance to the sun has no effect on eccentricity.

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Ellipses

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  1. Ellipses

  2. Ellipse • An ellipse is a closed curve around two fixed points called foci. • Earth, and all the planets, revolve around (orbit) the sun in an eccentric, elliptical orbit; However, the distance to the sun has no effect on eccentricity. • The sun is one of the two focal points of these orbits.

  3. Most ellipses have eccentric orbits. • Eccentricity is how far off something is from circular. • The formula for calculating eccentricity is: distance between foci Length of the major axis • The major axis is the longer of the two diameters of an ellipse.

  4. The minimum eccentricity an ellipse can have is ‘0’, a perfect circle. • The highest eccentricity an ellipse can have is ‘1’, a straight line. Therefore, as an ellipse approaches a straight line, the eccentricity increases from 0 to 1. • A circle is a geometric figure that is equidistant in all directions . . . Eccentricity = 1 Eccentricity = 0

  5. As the two focal points get farther apart, the eccentricity increases.

  6. Creating an eccentric ellipse • Materials: • Paper with a straight line drawn lengthwise down the center with the center marked. • Cork board • Two push pins (foci) • String (to represent Earth’s orbit) • Ruler (to measure distance between foci and length of major axis)

  7. Procedures for ellipses: • Using push pins, attach paper to cork board. • Place push pins 3cm apart from the center of the paper (1 ½ cm from center in each direction) • Loop the string around the pins and draw an ellipse using the string as a guide. • The distance between the pins is the distance between the foci (d). • The length of the major axis is the length of the diameter along the line (L). • Calculate the eccentricty: e = d/L

  8. Summary • The Earth orbits around the sun in a slightly eccentric ellipse. • Eccentricity is calculated by using the formula: Distance between foci (d) Length of major axis (L) • The degree of eccentricity is determined by the distance between the foci; as the foci get farther apart, the eccentricity increases from 0 (circle) to 1 (straight line).

  9. Motion in the Solar System • Put the following heading on a piece of loose leaf paper (1 sheet for every 2 people): • Name - Date • Page 407, Q 10 – 13 - Period • Get a black Earth Science book off the shelf. • Answer the above questions using either complete sentences or a T-chart.

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