18. CYCLOID and ASTRONOMY

a. Construct a cycloid type curve: i.e. figure out how to draw a locus of points C on a circle rolling along a line. Or the locus of points on a circle moving around the inside or outside of another circle.

b. Use this idea to model the motion of the Earth and Venus around the Sun. (Assume orbits are circles, and the distance from Earth to Sun is 93 million miles, and Venus to sun is about 60 million miles. Venus also takes about 240 days to orbit the Sun.)

c. Construct a model of the moon revolving around the Sun. Approximate the path of the Earth by a continuous ellipse with one focus at the Sun.