ASTR 100 (McGaugh)
Homework #2 solutions

Chapter 1, Problem # 7

There are many possible experiments which could test for the existence of telepathy. Here is one example: Create a set of four cards with four different geometric shapes on them: a circle, a square, a triangle, and a star. Two volunteers are used for the experiment. They sit in separate rooms so that they cannot see or hear one another. The researcher shows the first volunteer one of the four cards, chosen at random, and the second volunteer writes down what they think the card is. The researcher records which card was shown to the first volunteer. This process is repeated 200 times, and then the researcher's list and the second volunteer's list of cards are compared. By random chance, the second volunteer should guess the right card 25% of the time. If the volunteer gets the card right substantially more than this, that is evidence that telepathy exists.

Chapter 1, Problem # 10

(a) measurement: 124 mm
error: 1 mm
accuracy: 1 part in 124 = 1/124 = 0.008
% error = accuracy × 100 = 0.8 % error

(b) If we know someone's birthday month, then the measurement is accurate to 1 part in 12, since there are 12 months in a year.
accuracy: 1 part in 12 = 1/12 = 0.08
% error = accuracy × 100 = 8 % error

(c) measurement: 560 G
error: 17 G
accuracy: 17/560 = 0.03
% error = accuracy × 100 = 3 % error

(d) measurement: 1012 grains
error: 1012 grains
accuracy: 1012 parts in 1012 = 1 part in 1 = 1012/1012 = 1
% error = accuracy × 100 = 100 % error

(e)40,000 to 60,000 people is equivalent to 50,000 ± 10,000.
measurement: 50,000 people
error: 10,000 people
accuracy: 10,000 parts in 50,000 = 1 part in 5 = 1/5 = 0.2
% error = accuracy × 100 = 20 % error

To arrange these in order of least accurate to most accurate, note that the least accurate measurement is the one with the greatest percent error. So the answer is d,e,b,c,a

Chapter 2, Problem # 3

If you are standing facing the north at night, then
(a) assuming that you are in the northern hemisphere, a star just above the easter horizon will move higher in the sky and behind you. It reaches its farthest point behind you when it is highest in the sky. Then, the star moves down toward the western horizon and back forward toward you until it sets in the west.
(b) a star just above the western horizon will set in the west within a short period of time.
(c) the north star will not move appreciably during the night.
(d) a star just below the north star will move in a circle counterclockwise about the north star.

Chapter 2, Problem #10

Chapter 3, Problem #1

(a) When Galileo saw the fully lighted side of Venus from the Earth, this showed that Venus was on the opposite side of the Sun from the Earth. This observation proved that the Ptolemaic system was wrong since the Ptolemaic system said that Venus would always be between the Earth and the Sun.

(b) In the Copernican system, Venus goes around the Sun in an orbit closer to the Sun than the Earth's orbit. This orbit for Venus would mean that when it was farthest away from the Earth, it would be on the opposite side of the Sun from the Earth and thus would appear fully lighted to an observer on the Earth. This is consistent with Galileo's observation that when Venus appeared small it was fully lighted. The Copernican system also predicts that when Venus was closest to the Earth it would be on the same side of the Sun as the Earth and thus would show a crescent-lighted or new phase to an observer on the Earth. This is consistent with Galileo's observation that when Venus appeared largest it was crescent lighted.