BUCKNELL UNIVERSITY
Astronomy 102 - Final Exam, Solution
Part I: answer all 16 questions (48 points total+2 points
for name & seat#)
1. This course covered the following topics:
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a. how stars affect the destiny of humans
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b. how the science that we do on earth explains what goes on in the
universe
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c. how extra-terrestrial beings seeded the earth with life.
2. Light with 800 billionths of a meter distance between a crests of an
electromagnetic wave is
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a. red
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b. blue
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c. invisible
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d. orange.
3. After 10 billion years of fusing hydrogen into helium the sun may become
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a. a black hole
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b. a red giant
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c. the center of an enormous explosion that will result in the formation
of a white dwarf that will blow up in a supernova of type I.
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d. a pulsar.
4. The constellation of Leo, the lion, (Zodiac sign for August) may
rise at sunset on
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a. May
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b. February
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c. November
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d. the evening of December 24.
5. Some stars seem to move uniformly around Polaris because
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a. earth is spinning uniformly on its axis
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b. Polaris pulls the stars but they try to move by inertia, same as the
planets as they move around the sun
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c. the earth goes around the sun once every 365 days
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d. the earth is round.
6. The temperature of the solar surface is roughly
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a. 10,000 degrees F
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b. 5000 degrees F
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c. 500 million degrees K
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d. 10 billion degrees C.
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7. Lines of increased brightness in the rainbow spectrum of an O2 star
are probably due to
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a. Magnetic sun spots on the surface of that star
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b. Absorption of some photons by atoms in the star's atmosphere
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c. Emission from helium atoms in the star's chromosphere
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d. excited hydrogen atoms in the star’s corona.
8. In the center of the sun energy from fusion of hydrogen into helium
is released in the form of
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a. neon nuclei
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b. gamma rays
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c. coldness
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d. ultra sound waves.
9. We find the distance to the closest star
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a. by sending a space probe to Sirius, the dog star
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b. by bouncing a laser beam off the closest star, Proxima Centauri
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c. by observing a star in fall, and then in spring
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d. by measuring the Doppler shift of the lines from that star, and then
using Hubble’s law to determine the distance.
10. Neutron stars that rotate around their axis may be observed as
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a. continuum radiation in the radio part of the spectrum
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b. planetary nebulae
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c. white dwarfs
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d. regular pulses of light.
11. The galaxies that we see and our galaxy have a similar chemical composition
. This may imply that
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a. the mass of all galaxies is roughly the same
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b. all galaxies started out at roughly the same time
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c. everything that happened in our galaxy must have also happen in other
galaxies.
12. Edwin Hubble discovered the following
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a. the distance to the nearest galaxies
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b. the redshift of absorption lines from galaxies
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c. the fact that the further away a galaxy the fastest it seems to receed
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d. all of the above.
13. A blue photon is emitted from a galaxy 1000 Mpc away. If the Hubble
constant is 75 km/s/Mpc we may see this photon now as
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a. a microwave photon
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b. an infrared photon
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c. a visible photon
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d. a photon with the same frequency at which it was emitted.
14. At t~1 seconds after the big bang the universe was made of mostly
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a. electrons, neutrons, protons and neutrinos
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b. X-bosons
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c. quarks and electrons
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d. W and Z bosons
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15. The no boundary hypothesis asserts that
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a. time reversed itself once the universe reached very high temperatures
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b. we may be able to see our own galaxy as it was billions of years ago
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c. the big bang have had no initial time t=0
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d. the universe started from black-hole like singularities that managed
to start the big bang because of quantum fluctuations
16. Using a CCD camera we used one of the following steps in finding the
distance to stars
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a. we counted the photons from that star and subtracting the photons from
a nearby star
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b. we counted the photons through the yellow and blue filters
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c. we counted the photons through the red and blue filters
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d. we counted the photons through the yellow and green filters.
Part II: answer all 5 questions (50 points)
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(10 points) For a few seconds "Gamma Ray Bursters" (GRBs) shine with luminosity
1017 (!!!) times greater than that of the Sun. If such a GRB
were to appear in our sky as bright as the Sun, how far away from us must
it be located?
This problem is the same as the one in HW#4 prob. #1.
Same brightness = The power of the sun / 4 p
r*2 = The power of the GRB / 4 p
r2
Where r* is the distance to the sun (1 A.U.) and r is the distance to
the GRB.
Solving for r:
r=r* sqrt { Power of the GRB/ Power of the sun} = r* sqrt{1017}
= 3.2 x 108 A.U.
2. Two stars that appear four second of arc from each other in the night
sky have the following absorption lines: One of the stars has an absorption
line at wave length 486.08 nm and the other star has an absorption line
at wave length 486.12 nm. Both lines are due to the same atomic transition
with rest frequency of 486.10 nm.
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(5 points) Assuming that both lines are from the same atomic transition,
describe the motion of the stars (no numbers needed).
One is moving away from us while the other is moving towards us.
b. (3 points) Calculate the speed of
these stars.
Using the Doppler formula (see exam beginning):
{486.10nm – 486.08nm}/486.10nm = V / 3 x 108 m/s
Solving for V:
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V=12,000 m/s.
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(2 points) If both stars are 10 pc from us, how far are they from each
other?
Using trigonometry: The apex angle is 4", so half that angle is 2", We
may therefore find half the distance between the stars:
X=10 pc x sin(2/3600)= 10-5 pc
And the distance between the stars is 2 x 10-5 pc.
3. You observe an A2 star:
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(4 points) What is the color of this star? (Peak brightness: Red? Yellow?
Green? Blue?)
From the book: T=7500-10,000K. Within this range A2 is the third hottest
out of 10 categories (A0,A1, etc.). So the temperature is in the range
9500 – 9250K (we may use the middle of that range, 9375K.). Using Wein’s
law the color is
WL=2.9 x 106K nm / 9375K = 310 nm.
That’s in the ultra violet, which means that the star appears bluish.
b. (3 points) What is it's surface temperature?
From a: 9375K.
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(3 points) Given that the luminosity of the star is 8 x 1027
Watt and its mass is 7 x 1030 kg, what is its average density?
Density=Mass/Volume. To find the volume we have to find the radius of
the star. That may be found from the area of the star, 4pr2
. We may find that because we know the power from the star, and
the power from each square meter = sigma T4. So the power from
the whole surface is:
4pr2 sigma T4 = 8
x 1027 Watt. We find r, and substitute into
D=Mass/(4pr3/3)
We get : 950 Kg/m3 .
4. (10 points) Two stars have the same exact brightness. The peak of
the black body spectrum of the first star is blue and that of the second
star is red. From parallax measurements we know that both are at the same
distance from earth. What types of stars might these be?
Since the stars have different colors and similar brightness they CAN’T
be two main sequence stars. So they may be
A red giant and an O star
Or:
A white dwarf and an M star
Or:
(an interesting suggestion from one of your peers)
a red giant and a variable star.
5. (10 points) According to a certain theory of the "big-bang" the universe
is slowing down its expansion, or at least NOT speeding up its expansion.
Some measurements show that the age of globular clusters is 15 billion
years. Assuming that the Hubble constant is 75 km/s/Mpc to a very
high accuracy, can the theory be rejected? Explain your reasoning
in one-two sentences.
Yes. The theory can be rejected.
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If the Hubble constant is indeed accurately measured to be 75 Km/s/Mpc
you would get a universe that is 13 billion years old. If we hypothesize
that the universe is slowing down its expansion, this number is an OVERESTIMATE
(lab#8), i.e. the universe is LESS than 13 billion years old. So this is
INCONSISTANT with the measurement of the age of globular clusters, and
the hypothesis can be rejected! (As of yet the Hubble constant is
NOT known to such a great accuracy, but several researchers are getting
the errors to be fairly small.)