## Physics 109N Homework #2

Due Tuesday September 17, 2:00 p.m.

1. There will be an eclipse of the Moon on the 26th of this month, at full Moon. Could there ever be an eclipse of the Moon when the Moon is only half full? Show the Earth, Moon and Sun on a diagram to support your argument.

2. Find the North Star, Polaris. Now, find the angle of Polaris above the horizon by pointing a pencil at Polaris and having your partner measure the angle between the pencil and a horizontal line running directly beneath the pencil. Draw a sketch of the Earth, yourself, and Polaris and explain how the angle you measured relates to where you are on the Earth. Hint: what would this angle be at the North Pole? At the Equator?

3. (a) Explain, with a diagram, what is meant by the "Ecliptic". What is the "Zodiac"?

(b) Find from a calendar the dates of the Winter Solstice, the Summer Solstice, the Spring Equinox and the Autumn Equinox. Draw a sketch of the Earth's path around the Sun, showing where it is on these four days, including an indication of the angle between the North Pole-South Pole axis and the direction to the Sun.

(c) Count the days exactly in the four quarters of the year between solstices and equinoxes. Are these periods all the same length? Would you expect them to be? Explain.

4. Zeno of Elea argued that in a race between Achilles and the Tortoise, if Achilles runs ten times faster than the Tortoise, he will nevertheless never catch up if the tortoise is given 100 yards start. The argument is that when Achilles has covered this 100 yards, the Tortoise is 10 yards ahead. When Achilles has covered this ten yards, the Tortoise is 1 yard ahead. When Achilles has covered this 1 yard, the Tortoise is 1/10 yard ahead. Obviously, this goes on for ever! So he can never catch up. Explain carefully in your own words what's wrong with this argument.