Download Lab 2

Astronomy 115
Name(s):
Lab 2: Timekeeping and angles
Objective: In this lab, you will discover the connection between angles and
timekeeping, both of which are fundamental to astronomy.
The hours
1. a. How many degrees are in a circle (such as the equator around the Earth)?
b. Given that the Earth rotates on its axis once per 24 hours, how many degrees
does the Earth rotate in one hour? Another way to look at this question: how
many degrees of the sky disappear over the western horizon every hour?
2. Our latitude is given as 47.5° N; what does that indicate about our relative
position to the equator and the North Pole? If the Earth were twice as large as it it
today, would our latitude change?
b. What is the maximum latitude possible on Earth? Hint: see the globe.
c. What is our approximate longitude, and what hemisphere designation are
we in?
d. What is the maximum longitude, and why does this value differ from the
maximum latitude?
3. a. When you get the chance, go check out the sundial in the OCE&E courtyard
on the south part of campus. Local noon is obviously when the Sun is as high as
it gets in the sky that day (also called “Sun transit”). In what compass direction is
the Sun at noon? Is the sundial’s time accurate? If not, estimate how many
minutes the sundial is “off”.
b. Assuming that the sundial is set up correctly, explain this discrepancy.
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 and hours
4. a. Find the Foucault pendulum. What is the significance of this pendulum?
In other words, what does it show? Hint: Read its explanatory plaque.
b. How does it do that? I mean: there’s nothing twisting the cable to the ceiling,
yet it precesses...how come?
5. Check out the analemmic sundial on the side of the building facing Pacific
Avenue. Note that like the “traditional” sundial you’ve already seen, you can tell
time by it. In addition to the time, what else can you read from it? Hint: How do
the metal “braces” help? Why does this work?
The planetarium, diurnal motion, and angles
Once we’re inside the planetarium, I’ll demonstrate the cardinal directions,
diurnal (day/night) motion and constellations in the night sky. It will be dark,
so try to take notes the best you can, or write these next questions up after class.
6. a. I will display the celestial equator, the celestial North Pole and its coordinate
grid. What Earth-bound coordinate system does this resemble? In fact, the terms
right ascension (RA) and declination (dec) will be used to describe a point in
the sky. To what attributes of the Earth-bound coordinate system are these terms
analogous?
b. What are the units of declination? How is the hemisphere indicated?
c. What are the units of right ascension? What is the range of the right
ascension? Why do you think these units might be used for this attribute?
7. a. I will display the ecliptic, and show some planets and the Sun, then move
them forward in time. What defines the ecliptic? Is the ecliptic the same thing as
the celestial equator?
b. The ecliptic intersects the twelve Zodiacal constellations (e.g., Aries,
Taurus, Gemini, etc.); assuming each constellation is equally large, how many
degrees does each Zodiacal constellation subtend? So, roughly, how many
Zodiacal constellations disappear over the western horizon each hour?
c. On Earth, the British navy defined zero degrees longitude. What point defines
zero hours RA in the sky?
8. a. I will display the altitude and azimuth (altaz) coordinate system. What units
does it use? What do you notice is different about this system, compared to the
other two systems? Hint: Does this set of gridlines move? What are the
advantages of this system? What are the disadvantages?
b. Would the altaz coordinate system be used by textbooks to describe where to
find a star? Why or why not?
9. I’ll point out some common constellations, and set the sky into diurnal motion.
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? Are some stars (and constellations) visible all night?
10. 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?
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.
11. 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
12. Draw the location of the Sun as accurately as possible on figure 3.
13. 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.
14. 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.
15. 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
The annual cycle
As you have seen, the apparent motion of the Sun, from noon to noon compared
to the background stars, is west to east across the sky.
16. a. When viewed from high above the North Pole of the Earth, does the Earth
revolve around the Sun clockwise (CW) or counterclockwise (CCW)? Again,
viewed from high above the North Pole, does the Earth rotate on its axis
clockwise (CW) or counterclockwise (CCW)?
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)
17. Given the diagram on the previous page, then, how come news reports always
mention that the vernal equinox (or for that matter the autumnal equinox or
either of the solstices) occurs at a particular time and day? This year, the vernal
equinox was at 4:01 a.m., March 20. What definition of “equinox” allows this
kind of precision?