Solutions for Assignment #2 (Part of Chapter 2 and most of Chapter 3)

1.) In this diagram (click here), the yellow region on the right represents the Sun, the blue circle represents the Earth, and the white circle represents the Moon.
When the Sun, Earth, and Moon are in this orientation, what phase of the moon will people on Earth see?

a.) "Full" moon
b.) "New" moon
c.) "Quarter" moon
d.) "Crescent" moon
Answer: c, "Quarter" moon

2.) From the point of view of people in the northern hemisphere, how does the Sun's path across the sky vary throughout the year?
Answer: At the winter solstice, the Sun rises in the southeast and sets in the southwest. As the months go by, the directions shift more northerly, until the summer solstice. After the summer solstice, the directions shift more southernly, until the winter solstice. Then, the cycle repeats. During the daytime on the winter solstice, the Sun does not rise very high above the southern horizon. As the months go by, the Sun rises higher during the daytime, until the summer solstice. After the summer solstice, the Sun's height above the southern horizon during the daytime decreases, until the winter solstice.

3.) If you could change the Earth's motion, which of the following changes would cause the Earth to cease having seasons?

a.) Make the Earth's orbit perfectly circular
b.) Eliminate the Earth's tilt (i.e. the Earth's equator would be in the same plane as the Earth's orbit)
c.) Stop the Earth from rotating on its axis
d.) All of the above
Answer: b, eliminate the Earth's tilt. (Answer c would cause the Earth's day to last a whole year.)

4.) Regarding the Summer Solstice:

How does the summer solstice differ from any other day of the year?
Answer: On the summer solstice in the northern hemisphere (which occurs in June), the northern hemisphere is pointed more toward the Sun than on any other day. As a result, it collects more light and has longer periods of sunlight than on any other day of the year. Comparing the directions from which the Sun appears to rise and set throughout the year, these directions are most northernly at the summer solstice. Same for the Sun's maximum angle above horizon at noon. On the summer solstice in the southern hemisphere (which occurs in December), the southern hemisphere collects more light and has longer periods of sunlight than on any other day. The directions from which the Sun appears to rise and set are more southernly. Same for the Sun's maximum angle above the horizon at noon.
True or false: The ability to determine which day is the summer solstice requires modern observing technology.
Answer: False. The builders of Stonehenge and the Chaco Canyon Sun Dagger could do it using rocks, which are not "modern observing technology".

5.) In the earliest version of the geocentric model, the other planets moved in perfect circles around the Earth (in the earliest version, the other planets did not move in circles nested in circles, etc.) How did the predictions from this model disagree with observations?
Answer: The predictions said that planets such as Mars would always move in the same direction (relative to the celestial sphere). However, observations showed that Mars sometimes changed direction so that it moved "backwards" (retrograde motion). Later, its direction changed again so that Mars moved forwards again.

6.) Eudoxus (400 - 347 BC) and Kepler (1571 - 1630 AD) both worked on conceptual models in which the planets moved in perfect circles around the center of the solar system. There are 2 important differences between their stories. 1.) Eudoxus thought the Earth was at the center of the solar system, while Kepler thought the Sun was at the center. 2.) When faced with the fact that the models didn't correctly predict the observations, they found differing "solutions". What were their solutions, i.e. how did they adjust their models (in 2 to 4 sentences)?
Answer: Eudoxus adjusted the existing model by adding additional spheres. So, his planets moved on spheres nested within several other spheres. Although this helped greatly, later observations of planetary positions didn't quite match the model's predictions (even after his model had been refined by subsequent people).
Kepler adjusted his initial model by changing the shapes of the planets' orbits around the Sun to make them elliptical. This helped greatly and the predictions lived up to the observations of the time (more later, when we get to Einstein and relativity).

7.) The distance between the Sun and Mars is 1.5 times the distance between the Sun and Earth. From Kepler's 3rd law, how long does it take for Mars to make an orbit around the Sun, in years?
Answer: Kepler's law: p² = a³, where p is in years and a is the distance from the Sun to the planet in AU (AU = astronomical unit = distance from Earth to Sun) so
p = square-root of (a³), so
p = 1.8 years (this differs slightly from the actual period, 1.88 years, because of round-off error)

8.) Galileo refuted the objections to the heliocentric model with elliptical orbits. List 3 of of his arguments (you don't have to explain all of the logic.)
Answer: 1.) The previous thinking was that if the Earth were moving, then it would leave behind the clouds and birds. Since the clouds and birds stayed with the Earth, the Earth must be stationary according to this logic. Galileo argued that objects that are currently moving will continue to move, unless they are affected by a force. The clouds and birds are currently moving alongside the Earth as the Earth makes its orbit, so they will continue to move along with the Earth and won't be left behind.
2.) The previous thinking was that heavens were perfect and unchanging. That implied that planets should have perfect orbits, which meant circular orbits. But, Galileo argued that the heavens are imperfect (ex: Sunspots, craters on the Moon, Tycho's "new star"), so it is OK for the planets to have imperfect orbits, such as elliptical orbits.
3.) The previous thinking was that if the Earth were moving, then humans would see changes in the angles between any 2 stars. Galileo argued that the stars may be so far away that the angles between them might change imperceptibly small amounts when the Earth moves.
4.) In addition, Galileo's telescope observations showed that Venus goes through all phases (full, gibbous, quarter, crescent, and new), which can only happen if Venus orbits the Sun rather than the Earth.

9.) Regarding the Scientific Method

List the steps in the scientific method.
1.) Observe something new or unexpected.
2.) Wonder why this happened (Some people do #1 and #2 together.)
3.) Develop a possible explanation (a hypothesis).
4.) Make a prediction that is based on the hypothesis.
5.) Test the prediction.
6.) If the prediction failed the test, go back to step 3; if the prediction matched the observation, go back to step 4, repeat cycle.
Suppose that you are following the scientific method to the point of performing an experiment that tests the prediction of your hypothesis. If the results of this test contradict your hypothesis, what do you do next?
Answer: Develop a new hypothesis and follow the steps from that point on
In contrast, suppose that the results of your test agree with your hypothesis. What do you do next?
Answer: Devise a new way to test your hypothesis (i.e. make a new prediction based on the hypothesis and then test the new prediction, then follow the steps from that point on). Notice that the cycle is infinite; you can never finish applying the scientific method.