Astronomy 100
Name(s):
Exercise 2: The UW planetarium trip
The University of Washington Physics and Astronomy Building houses a
wonderful planetarium, in addition to some other interesting displays. Use those
resources to answer the following questions.
Outside the planetarium
1. a. Find the Foucault pendulum. What is the significance of this pendulum?
In other words, what does it do?
b. How does it do that? I mean: there’s nothing twisting the cable to the ceiling,
yet it precesses...how come?
2. a. Check out the analemmic sundial on the side of the building facing Pacific
Avenue. Does it give the correct time? If it does not, suggest the reason(s) it may not.
b. In addition to the time, what else can you read from it? Hint: What is the
purpose of the metal “braces”?
3. a. How many degrees in a circle (such as the ecliptic around the Earth)? The
ecliptic is broken up into the twelve Zodiacal constellations (e.g., Aries,
Taurus, Gemini, etc.); assuming each constellation is equally large, how many
degrees does each Zodiacal constellation subtend?
b. How many degrees of the sky does one hour represent? Another way to look
at this question: how many degrees of the sky disappear over the western horizon
every hour?
The planetarium
4. Once inside the planetarium, I’ll demonstrate the cardinal directions, altitude
and azimuth, and the ecliptic. As the stars come out, notice that Polaris, the end
star on the handle of the Little Dipper, stays in place through the whole night,
while all the other stars revolve around it. What other measurement is equal to
the altitude of Polaris at any given location in the northern hemisphere?
5. a. I will change the latitude of you, the observer, so that we are at the equator.
On the same date and time, are all of the same constellations visible at the
equator as are visible in Seattle?
b. How about at the latitude of Invercargill, New Zealand, which is approximately
at the same latitude as Seattle, but in the southern hemisphere?
The lunar cycle
6. In the figure of the Moon below, indicate the direction of the Sun with an
arrow (point the arrow from the Sun to the Moon.
7. a. Telling time using the Moon: At what time of day would you expect to
observe a full Moon rising? Over which (eastern or western) horizon would it
rise?
b. At what time of day would you expect to observe a first quarter Moon setting?
c. At what time of day would you expect to observe a new Moon overhead?
A guide for naming the phases of the Moon:
If only a minimal crescent of the Moon is illuminated, it is a new Moon. If less
than half of the Moon is lit, it is a crescent Moon. A half-illuminated Moon is a
quarter (not half) Moon (first quarter occurs before full Moon, third quarter
occurs after). If more than half is illuminated, but the Moon is not full, it is
gibbous. If it is fully illuminated, it is a full Moon.
When the lighted side’s apparent area increases from night to night, the Moon is
said to be waxing; when the apparent area decreases, the Moon is waning.
8. In the upper portion of the figure (which represents looking down on the
Earth and Moon from the celestial north pole), eight positions of the Moon
(labeled 1 through 8) are given in its orbit around the Earth. The lower part of the
figure shows what an Earth observer would see of the Moon at each of the
eight positions.
a. For each position on both parts of the figure, shade the dark and illuminated
portions of the Moon.
b. For the lower part of the figure, label each Moon's phase.
c. For the upper part of the figure, is the Earth rotating clockwise (CW) or
counterclockwise (CCW)? Indicate this with an arrow.
9. Night after night, in what compass direction does the Moon appear to move,
relative to the fixed stars? So does the Moon rise earlier or later each night? Does
this mean the Moon can rise during daytime as well?
10. From your phase drawings, why isn’t every new moon, when the Moon is
between the Earth and the Sun, coincident with a solar eclipse? In other words,
why isn’t the sun eclipsed every 28 or so days when there’s a new moon? Hint: a
related idea is the “
11. If your answer to the previous part is true, then, how do we ever see a fully lit,
full Moon? Shouldn’t some of its face toward us always be dark?
12. a. Does the Moon rotate on its own axis? Note: Rotate, not revolve.
Equivalent question: Does the Moon always present the same face to us on
Earth?
b. So what percent of the whole Moon’s surface should we be able to see and map
from telescopes on the surface of the Earth?
c. In fact, we have been able to map 59% of the Moon’s surface from Earth-based
telescopes (the rest was done by sending satellites around the “back”). How are
we able to see that much? Hint: look up “libration”.
The annual cycle
For the next figures, pretend that the stars are so bright and the Sun so dim that
the stars can be seen during the day and do not “wash out” the Sun, which we can
totally do in the planetarium.
On December 1 at noon, you are looking toward the south and see the Sun among
the stars of the constellation Scorpius (informally, “the Sun is in Scorpius”) as
shown in the figure below.
13. Two students are discussing their answers to the question “At 3 p.m. that
afternoon, which constellation will the Sun appear?”
Student 1 (Goofus): The Sun moves from the east through the southern part of
the sky and then to the west. By 3 p.m., it will have moved from being high in the
southern sky to the west into the constellation Libra.”
Student 2 (Gallant): You’re forgetting that stars and constellations will rise in the
east, move through the southern sky and then set in the west just like the Sun. So
the Sun will still be in Scorpius at 3 p.m.”
a. With whom do you agree? What argument convinced you?
b. So is it reasonable to pretend that the Sun is at a fixed position on the celestial
sphere from one day to the very next day, and is carried along its path in the sky
by the sphere’s rotation?
By carefully observing the sky night after night (which we will speed up in the
planetarium), we find that the celestial sphere rotates slightly more than 360°
every 24 hours. The figures below show the same view of the sky as the previous
one, except one day later and one month later, respectively (for comparison, the
gray constellations show the positions of the constellations on December 1 at the
same time).
Figure 3
Figure 4
14. Draw the location of the Sun as accurately as possible on figure 3.
15. Two students are discussing their answers to the question “Figure 4 shows the
same view of the sky one month later on January 1. Draw the location of the Sun
as accurately as possible on figure 4.”
Student 1 (Davey): The Sun will always lie along the dotted line in the figures
when it’s noon.
Student 2 (Goliath): I don’t know, Davey; we saw in question 8 that the Sun’s
motion can be modelled by assuming it is stuck to the celestial sphere. The Sun
must, therefore, stay in Scorpius.
Student 1 (Davey): If that were true, then by March the Sun would be setting at
noon. The Sun must shift a little along the celestial sphere each day so that in 30
days it has moved to the east in the next constellation.
Whom do you believe? What convinced you? And sketch the Sun in its proper
location in figure 4.
16. Why is it reasonable to think of the Sun as attached to the celestial sphere
over the course of a single day as suggested in question 5 even though we know
from question 7 that the Sun’s position is not truly fixed on the celestial sphere?
Now consider the whole celestial sphere; the Sun’s position on the celestial
sphere on December 1 is shown in figure 5 below, among the stars of the
constellation Scorpius.
17. a. Draw where the Sun will be located on the celestial sphere on January 1.
Label this position “Jan. 1”. Then locate and label the Sun’s position for February
1, March 1, April 1, May 1, June 1, July 1, August 1, September 1, October 1 and
finally, November 1.
b. Clearly, the line shown in figure 5 going through the Zodiac is the ecliptic, the
“pathway” of the Sun. And the length of time it takes to complete one cycle is
_________________________ .
Figure 5: The celestial sphere
From the viewpoint of the Earth, it appears that the Sun revolves around the
Earth once per year. The Sun follows a nearly circular “orbit” around the Earth
(from the perspective of the Earth), which the ancients named the ecliptic. The
constellations along the ecliptic, called the Zodiac, allowed the ancients to
predict what part of the sky the Sun inhabited during various portions of the year.
The apparent motion of the Sun, from noon to noon compared to the background
stars, is west to east across the sky.
18. a. When viewed from high above the North Pole of the Earth, does the Earth
move around the Sun CW or CCW? How does this compare to the direction of the
Earth’s rotation?
b. This is no mere coincidence. What is the deeper reason why the two motions
(rotation and revolution) are similar? (Hint: consider the current origin
theory of the solar system)
19. Given the diagram on the previous page, then, how come news reports always
mention that the autumn equinox (or for that matter the vernal equinox or
either of the solstices) occurs at a particular time and day? This year, the
autumn equinox was at 1:44 p.m. last Sunday. What definition of “equinox”
allows this kind of precision?