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.

• The sun is one of the two focal points of these orbits.

• 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.

• 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 = 0 Eccentricity = 1

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

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)

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

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).

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.