1. Kepler's first law of planetary motion is:
The path of each planet is an ellipse with the sun at one foci.
a. In its orbit around the sun, the closest the earth comes
to the sun is 91,500,000 miles. Its farthest point is
94,500,000 miles. If the sun is at one focus, find the
length of the major and minor axes.
Major axis = ____________
Minor axis = ____________
b. The American artificial satellite Explorer followed an
elliptical orbit around the earth. At its closest point
to the Earth (perigee) it was 230 miles away. Its
farthest point (apogee) was 1700 miles away. If the
radius of the Earth is 4000 miles and the center of
Earth is at one focus, find the major and minor axes of
this orbit.
Major axis = ____________
Minor axis = ____________
2. If the ellipse is rotated about the major axis, we get an
ellipsoid. A football is an example of an ellipsoid.
3. If you have ever been on a tour of the Capitol in Washington, D.C. ,
you may have been amazed by a demonstration given by
the guide. After placing the group of people on a brass
plate in the floor of the old House of Representatives, the
guide walks about 100 feet away and whispers. You can hear
every syllable clearly! ! The reason for this is that the
ceiling is elliptical and the sound waves are reflected so
that they focus upon a single point. The very weak sound
waves of the guide's voice, going out in all directions,
were reflected through the other focus (both marked by brass
plates).
4. Elliptical Billiard Table
A. A ball is hit so as not to pass between the foci. With a
ruler and protractor, draw the path of the ball for at
least 5 reflections, and then draw a conclusion about its
path.
B. The ball is hit between the foci. Follow the path of the
ball for at least 5 reflections. Make a conclusion about
its path.
C. Now start the ball at a focus, Follow its reflections.
What does its course approach after a few rebounds?
