Chapter 3

Suppose you lived on a planet where the month was 25 days long and the year was 330 days long. Invent a calendar (similar to that of the Mesopotamians) in which each year has a whole number of months and the average length of the year is 330 days.

Describe a way in which Eudoxus's model could have explained the motion of the Sun, both during a day and throughout a year.

Suppose the Earth had a shape like a football with the long axis lying in the plane of the Earth's equator. What effect would this shape have on the constancy of the appearance of the Earth's shadow on the Moon during eclipses?

Greek astronomers rejected Aristarchus's idea that the Earth moved around the Sun. They argued that the separations of stars would change during a year if the Earth moved. Describe an alternative explanation for the unchanging shapes of the constellations that works for a moving Earth.

Suppose the motion of a planet on its epicycle was in the opposite direction to the motion of the epicycle on the deferent (that is, clockwise versus counterclockwise \(.\) Would retrograde motion occur for the planet?