Introductory Astronomy SCI-103 Fall 2014
Exam #1
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Do three of the following four problems
1. The Sun has a radius of 696,000 kilometers and the Earth has a radius of 6.378106 meters. How many times
larger is the Sun’s radius compared to the Earth’s radius? Show your work.
Radius of Earth  6.378  106 m  6.378  103 km
Radius of Sun in km
696,000 km

 109
Radius of Earth in km 6.378  103 km
The Sun’s radius is 109 times larger than the Earth’s radius.
2. Jupiter is now about 9.03108 kilometers from the Earth. How many AU is that?
1 AU


9.03  108 km  9.03  108 km  
6
  6.02 AU
150  10 km 
9.03108 kilometers is equivalent to 6.02 astronomical units.
3. At a typical walking speed of 5 km/hour, how long would it take to walk to the Sun, if you could? Express your
answer in years.
t
d 150  10 6 km

 30  10 6 hr  3,422 years
km
v
5
hr
It would take 3,422 years to walk to the Sun at a walking speed of 5 km/hr.
4. If the Earth were the diameter of a basketball (9 inches), How far away would the Sun be? Express your answer
in miles.
Model #1 Model #2

Actual #1 Actual #2
Model Earth Diameter Model Sun Distance

Actual Earth Diameter Actual Sun Distance
9"
x

2  6,378 km 150  10 6 km
9"
x
 150  10 6 km
2  6,378 km
x  1.06  105 inches  1.67 miles
The Sun would be 1.67 miles away if the Earth were the 9 inch diameter of a basketball.
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5. On the image of the celestial sphere below, assuming that the observer is located in Bangkok, Thailand (14 N),
draw or label the following:
a. The position of the zenith
Meridian
Celestial Equator
b. The meridian
c. The horizon
d. Polaris (the NCP really)
Zenith
e. The SCP
f. The Celestial Equator
g. The path of a northern star
h. The path of a southern star
NCP
W
14 altitude
S
N
-14 altitude
SCP
E
Path of Southern Star
Horizon
Path of Northern Star
The portion of the celestial sphere appears to the right.
Answer the three questions that follow.
6. What do the dashed lines represent?
The dashed lines represent the boundaries of the
constellations.
7. The solid lines that connect the stars (e.g. Alkaid to
Mizar to Alioth etc.) identify the Big Dipper. Is it true
that the Big Dipper is a constellation? Explain your
answer.
It is not true that the Big Dipper is a constellation. The Big Dipper is an asterism – an easily recognized pattern
of stars. A constellation is an area in the sky with internationally-agreed-upon and well-defined boundaries in
RA and dec.
8. What do the other straight lines on the map represent?
The other straight lines on the map represent the celestial coordinates of Right Ascension and Declination.
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9. You are observing from the location on the world map below designated as H. Draw the apparent motion of the
stars looking North, East and South in the boxes provided below. Include all relevant time and quantitative
information.
Lat = 20N




Stars appear to rotate CCW
around Polaris once every 23h
56m 4.09s
The altitude of Polaris is 20.
Stars are above the horizon for
more than 12 hours. Some are
circumpolar.
Some northern stars can reach a
high maximum altitude.
60
50
40
Circumpolar boundary
Altitude
Never set
30
Polaris (NCP really)
20
10
North
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

20
20 N Latitude
Stars are above the horizon for
about 12 hours
The Celestial Equator intersects
the horizon due east.
20
Celestial Equator



20 N Latitude
Stars are above the horizon for less than 12 hours
The SCP is 20 below the horizon.
Southern stars reach only a low maximum altitude
20
20
East
South
Circumpolar
Region
(never rise)
You are observing from Melbourne, Australia (38S). Answer
the following questions. You may use the figure below to
help answer the questions.
SCP, -20 altitude
Zenith
10. What would be the maximum altitude of the Celestial
Equator? What would its azimuth be at max. altitude?
Cel. Eq.
SCP
The maximum altitude of the Celestial Equator would
be 52 with an azimuth of 0
38
52
11. Would a star at declination +70 be visible? If yes
what would be its maximum altitude?
A star at declination +70 would not be visible. It
would never get closer than -18altitude.
52
38
S
N
-38
-52
Star
70 dec
Star
-50 dec
12. Would a star at declination -50 be visible? If yes
what would be its maximum altitude?
NCP
90 dec
Cel. Eq.
Nadir
A star at declination -50 would not be visible. It would never get closer than -12 altitude.
13. How long would a star at 0 declination be above the horizon?
A star at 0declination will be above the horizon for 12 hours for all observers since it is on the Celestial
Equator.
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14. In about 300 B.C.E. Aristotle wrote “Of these fixed poles the one is always visible, being above our heads in the
northern region of the sky, and is called the Arctic Pole; the other is always hidden beneath the earth to the
south and is called the Antarctic Pole.” Why did Aristotle not mention that Polaris is a fairly bright star located
near the Arctic Pole? Answer in a couple of sentences.
Aristotle not mention that Polaris is a fairly bright star located near the Arctic Pole because Polaris was not near
the Arctic Pole (now known as the NCP) at that time. Precession is the slow wobble of the Earth’s rotation axis
over a 26,000 year cycle. Due to precession, Polaris is now near the NCP, but was not at the time of Aristotle.
15. The date is April 15 and the Sun is rising 27 away from due east. What is the Sun’s rising azimuth?
Since the date is April 15, after the Spring Equinox on Mar 22 when the Sun crosses the Celestial Equator
heading north, the Sun must be in the northern celestial hemisphere. Thus, as for all stars in the northern
celestial hemisphere, the Sun must be rising north of east. So the azimuth that is 27 away from due east and is
north of east is 90 - 27 = 63 azimuth. So the Sun must rise on April 15, in this problem, at 63 azimuth.
16. Which of the following locations is closest to the north celestial pole?
a. RA = 14 h
dec = -85
d. RA = 14 h
b. RA = 0 h
dec = -43
e. RA = 8 h
c. RA = 23 h
dec = +43
dec = +85
dec = -2
17. Which of the following coordinates in your local horizon system (in Syracuse, NY at 43 N) is closest to the
zenith?
a. Az. = 180, Al. =43
d. Az. = 35,
Al. = 2
b. Az. = 273, Al. =52
e. Az. = 3,
Al. = 48
c. Az. = 90,
Al. = 90
Toward Sun
18. The figure at right shows a stick and its shadow at noon for
an observer in the continental U.S. on Sep 22. How will
the shadow length at noon change during the course of the
following week?
a. The Shadow length will be longer than on Sep
22.
b. The Shadow length will be the same as on Sep 22.
c. The Shadow length will be shorter than on Sep 22.
d. The shadow will not appear because we are in
Syracuse and the Sun never shines in Syracuse.
On Sept 22 the Sun is crossing the Celestial Equator and
heading south. So the Sun will be moving deeper into the southern celestial hemisphere. This means that the Sun
will have a lower maximum altitude each succeeding day (until it reaches the Winter Solstice) and it will produce a
longer shadow each succeeding day.
The date is Dec 22. You observe that the Sun sets that day along the horizon as shown in figure below.
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19. One week later will the Sun set at
a. the same location along the horizon,
b. to the right of the location shown above, or
c. to the left of the location shown above?
The Sun on Dec 22 has reached its southernmost declination and is starting to move north in the celestial
sphere. Thus it will set just a bit further north each succeeding day, until it reaches the Summer Solstice. Since
the image above must be looking generally west, the Sun will set to the right, towards the north, one week later.
The image below illustrates the path of the Sun across the sky on three different days as seen from Syracuse, NY.
A
B
East
C
South
West
20. Which of the paths labeled A, B or C, could represent the path of the Sun on Mar 22?
a. A
d. More information is needed to answer
the question
b. B
c. C
e. None of the above.
21. Which of the paths labeled A, B or C, could represent the path of the Sun the Winter Solstice?
a. A
d. More information is needed to answer
b. B
the question
e. None of the above.
c. C
22. Which of the paths labeled A, B or C, could represent a day with 9 hours of daylight?
a. A
b. B
c. C
d. More information is needed to answer
the question
e. None of the above.
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Use the whole sky Map below to help you answer the following questions.
All Sky Map
B
C
East
A
Celestial Equator
West
Ecliptic
D
12 Hr RA
6 Hr RA
0 Hr RA
18 Hr RA
12 Hr RA
23. What is the name of the point labeled D? ____Winter Solstice____
24. When the Sun is at point A where will it rise along the local observer’s horizon? (Assume a northern
hemisphere observer.) Justify your answer using properties (rules) of the celestial sphere.
When the Sun is at point A it is on the Celestial Equator and will act like a star on the Celestial Equator for that
day. All stars on the Celestial Equator rise due east, set due west, are above the horizon for 12 hours andreach
an intermediate altitude. Thus the Sun will rise due east when it is at point A.
25. At which of the labeled points A through D will the Sun be above the horizon for the longest time for an
observer at Syracuse, NY?
The Sun will above the horizon for the longest time at pointy B for an observer at Syracuse, NY.
26. What is the declination of the Sun at the point labeled B? +23 ½  dec
27. At which of the labeled points will the Sun set to the south of west? Point D
28. At which of the labeled points will the Sun rise at 90azimuth? Points A and B.
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29. Define the solar day and the sidereal day and explain why they are different. Answer in three sentences.
The solar day is the time period from one noon to the next noon or
equivalently from the time the Sun transits the meridian to the next
transit. This time is 24 hours (on average).
The sidereal day is the time for the Earth to complete one full
rotation on its axis or equivalently from the time a star transits the
meridian to the next transit of that same star. This time is 23 hr 56
m 4.09s.
The solar day and the sidereal day are different because the Earth
is revolving about the Sun as it rotates on its axis. Thus if you
start your clock when the Sun transits the meridian , then one
sidereal day later you will be facing the same direction, but will
have moved about 1 around the Earth’s orbital path and not be
facing the Sun. See the figure. The Earth will have to rotate
eastward about another 4 minutes to realign the Sun with the meridian.
The Sun is located in the constellation of Sagittarius on as indicated on the map below.
Ophiuchus

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30. In what constellation will the Sun be found 6 hours after the time pictured above?
a. Aquarius
d. Ophiuchus
b. Capricornus
e. Scorpius
f. Libra
c. Sagittarius
g. Virgo
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Astronomy Formula and Constants Sheet for Exams
Conversions
Formulas
A
L

2D
360 
Main Sequence Lifetime t 
M
1010 yr
L
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