Astronomy 102 Practice Exam #2
Spring 2000
If this were a real exam, you would be advised here of the Exam rules:
“You may use only a writing instrument and a calculator while taking this
test. You may not consult any books, notes – neither on paper nor stored in
a calculator – nor each other. All of your work must be written on the
attached pages, using the reverse sides if necessary. Important equations,
numbers and conversion factors, used in the problems, are given in the
last pages as the Useful Equations sheet and the How Big Is That sheet,
where you’ll also find a graph pertaining to the sizes of white dwarfs and
neutron stars. The final answers must be indicated clearly. Exams are due
at 3:15, and will be returned to you during Thursday’s lecture.”
Name: __________________________________
AST 102 Practice Exam #2
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Spring 2000
1. List two independent pieces of evidence that indicate the presence of supermassive
black holes in the centers of quasars.
2. Knots in the jet of 3C 273 appear to move across the sky at a speed seven times that of
light. This is an effect of
F the breakdown of the special theory of relativity: the jet was ejected by a black
hole, and Einstein was wrong about black holes.
F general relativity: specifically, the large gravitational redshift for objects escaping
from black holes.
F geometry: as the knot moves further along the jet, the light from the knot gets a
larger "head start" on its trip to Earth.
F degeneracy pressure: the knot gets smaller as it increases in mass.
F each of the above effects plays a role.
F none of the above effects plays a role.
3. A bright star is seen to be orbiting with a companion that is nearly invisible but emits
detectable ultraviolet light. From the orbital speed and mass of the bright star, a mass
for the companion of 3x1032 gm is deduced. The companion object is most likely to be
F a normal star.
F a white dwarf.
F a neutron star
F a black hole.
F unknown; the evidence is ambiguous.
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4. A spinning black hole with the same mass as the Sun has 10% of its total mass stored
outside its horizon, in the form of rotating spacetime. How much available energy does
this represent?
F 1.8x1054 erg.
F 1.8x1053 erg.
F 1.8x1051 erg.
F 1.8x1016 erg.
F None of above.
5. The mass of an object appears to increase as its speed with respect to an observer
increases. This is a consequence of
F Einstein's special theory of relativity.
F Einstein's theory of the duality of wave and particle properties.
F Chandrasekhar's theory of relativistic degeneracy pressure.
F Schwarzschild's theory of the event horizon.
F all of the above.
F none of the above.
6. Sketch the appearance of a radio galaxy: show how it would look at visible
wavelengths, and again at radio wavelengths.
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7. Sketch the appearance of a quasar: show how it would look at visible wavelengths,
and again at radio wavelengths.
8. Supernovae happen because
F a pair of neutron stars, orbiting about each other at high speed, coalesce to form a
black hole, and release about 10% of their rest energy as radiation as they do.
F the outer parts of a rapidly-collapsing dead star bounce off of the horizon of a
black hole suddenly formed at its core.
F the outer parts of a rapidly-collapsing dead star are slung gravitationally around
the horizon of a black hole suddenly formed at its core, and are ejected at speeds
close to the speed of light.
F matter and antimatter annihilate each other in the center of the star, converting all
of their mass into a vast amount of light energy (according to E = mc2) and
exploding the star.
F any of above.
F none of above.
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9. The circumference of a 1.0 solar mass white dwarf is
F 4.4x1011 cm.
F 3.6x109 cm.
F 7.6x106 cm.
F 1.9x106 cm.
F none of above.
10. List two independent pieces of evidence that indicate the presence of a massive
black hole in the center of our Milky Way galaxy.
11. The circumference of a 1.0 solar mass neutron star is
F 4.4x1011 cm.
F 3.6x109 cm.
F 7.6x106 cm.
F 1.9x106 cm.
F none of above.
12. The Sun has a total lifetime of 15 billion years. The energy that the Sun radiates in its
lifetime is
F 1.8x1054 erg.
F 1.8x1053 erg.
F 1.8x1051 erg.
F 1.8x1016 erg.
F none of above.
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13. Describe briefly how astronomers measure the masses of pairs of astronomical
objects that revolve around each other.
14. If a gamma-ray burster were to occur in Rochester, it would destroy all life within
F Rochester.
F western New York.
F the Earth hemisphere centered on Rochester.
F about 3 light years of Earth.
F about 3000 light years of Earth.
F none of above.
15. In a few complete sentences, explain what is meant by the phrase, "black holes have
no hair."
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16. A bright star is seen to be orbiting with an invisible companion. From the orbital
speed and mass of the bright star, a mass for the companion of 3x1033 gm is deduced.
The companion object is most likely to be
F a normal star.
F a white dwarf.
F a neutron star.
F a black hole.
F unknown; the evidence is ambiguous.
17. Degeneracy pressure is due to
F the particle properties of the elementary constituents of matter.
F the wave properties of the elementary constituents of matter.
F the relativity of mass.
F the relativity of time.
F the absolute nature of the speed of light.
F all of above.
F none of above.
18. The black hole in a certain quasar accretes matter at a constant rate of 1 solar mass
per year. If it turns 10% of the mass into energy in the form of light, what is its
luminosity?
F 1.5x1015 solar luminosities.
F 1.5x1014 solar luminosities.
F 1.5x1013 solar luminosities.
F 1.5x1012 solar luminosities.
F All of above.
F None of above.
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19. In a few complete sentences, explain why there aren't any stars supported by proton
degeneracy pressure.
20. Check all the correct answers. Which properties among the following list can be
conserved during black hole formation?
F Mass.
F Electric charge.
F Magnetic field.
F Stellar type.
F Identity as a radio galaxy or a quasar.
F Identity as matter or antimatter.
F Spin.
F Luminosity.
F Efficiency.
F Wave properties.
F Particle properties.
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21. A black hole with mass 1.0 solar masses has a horizon with circumference equal to
F 18.5 km.
F 23.4 km.
F 26.2 km.
F 29.5 km.
F none of above.
22. You are looking down the rotation axis of a very massive, rotating black hole, shown
below, and can see a friend of yours in free fall toward the horizon. Your friend has told
you that he will fall in vertically along the plane of the horizon’s equator, aimed always
at the center of the black hole. Part of his path is indicated; sketch the rest of it.
23. The X-rays emitted by Cygnus X-1 or GRO J1655-40 are produced by
F electrically-charged particles that are about to fall through the black hole's horizon
at very high speeds.
F electrically-charged particles that have been ejected by the black hole in the form
of a pair of jets, travelling at very high speeds.
F the non-radial pulsations of the black hole's horizon.
F the swirl of spacetime just outside the black hole's horizon, where approximately
20% of the hole's total energy is stored.
F any of the above.
F none of the above.
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Spring 2000
24. At what speed would a green object (wavelength 5x10-4 cm) have to recede from you
to appear yellow (wavelength 5.5x10-4 cm)? Express your answer in km/sec, and show
your work.
25. A black hole candidate is found to have luminosity in the form of X-rays and gamma
rays of 100 solar luminosities. Assuming an efficiency of 10% for converting mass into
radiated energy, it is producing this power by swallowing matter at the rate
F 9.1x104 gm/sec.
F 4.2x1015 gm/sec.
F 2.0x1033 gm/sec.
F 3.1x1051 gm/sec.
F none of above.
26. The mass of an object whose horizon circumference is the same as the Sun's
circumference is
F 1 solar mass.
F 2.4x105 solar masses.
F 3.4x105 solar masses.
F 4.4x105 solar masses.
F none of above.
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Spring 2000
27. List three independent pieces of evidence that indicate the presence of a black hole
in GRO J1655-40.
28. A bright star is seen to be orbiting with a companion which is a strong source of
visible light. From the orbital speed and mass of the bright star, a mass for the
companion of 2x1034 gm is deduced. The companion object is most likely to be
F a normal star.
F a white dwarf.
F a neutron star.
F a black hole.
F unknown; the evidence is ambiguous.
30. The circumference of a 1.0 solar mass normal star is
F 4.4x1011 cm.
F 3.6x109 cm.
F 7.6x106 cm.
F 1.9x106 cm.
F none of above.
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31. A bright source of X-rays is detected. Astronomers searched the surrounding area
and found no visible light from stars or galaxies. This object is most likely to be
F a normal star.
F a white dwarf.
F a neutron star.
F a black hole.
F unknown; the evidence is ambiguous.
29. In a few complete sentences, explain why there is a certain maximum mass that
degeneracy pressure is capable of supporting, whether the pressure is from electrons or
neutrons.
32. A star is in orbit with speed 150 km/sec around an invisible companion. Your view
of the orbit is edge on, and you can observe an absorption line (rest wavelength 10-4 cm)
in the star’s spectrum. What is the longest wavelength you will observe for this
absorption line?
F 1.00000x10-4 cm.
F 1.00025x10-4 cm.
F 1.00050x10-4 cm.
F 1.00075x10-4 cm.
F 1.00100x10-4 cm.
F None of above.
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Spring 2000
33. A star is in orbit with speed 150 km/sec around an invisible companion. Your line of
sight makes a 60 degree angle with the plane of the orbit, and you can observe an
absorption line (rest wavelength 10-4 cm) in the star’s spectrum. What is the longest
wavelength you will observe for this absorption line?
F 1.00000x10-4 cm.
F 1.00025x10-4 cm.
F 1.00050x10-4 cm.
F 1.00075x10-4 cm.
F 1.00100x10-4 cm.
F None of above.
34. An explorer has returned from a trip to a black hole, claiming to have escaped after
becoming trapped inside the event horizon. As she explained, "I fell through the
horizon quite by accident, and that was scary initially, since like everybody else I was
taught that one can't get out from the inside of a black hole. Fortunately time is very
strongly dilated near the event horizon. With everything around me thus appearing in
slow motion it was no trouble to punch a new hole in the horizon and grab the edges
before I started to fall further. I managed to wriggle out through that hole, after which I
just reversed the polarity of the magnets in my space suit and let their repulsion by the
black hole's magnetic field push me away from the horizon to safety." What is wrong
with her story?
AST 102 Practice Exam #2
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Spring 2000
35. Check all the correct answers. The class of active galaxy nuclei includes the
following types of objects:
F blazars
F pulsars
F quasars
F gamma-ray bursters
F radio galaxies
F X-ray binaries
F Seyfert galaxies
F white dwarfs
F the Milky Way
F all of above
F none of above.
36. Check all the correct answers. All active galaxy nuclei have these observable traits in
common:
F Long, narrow jets stretching out from the center.
F Two radio lobes, arranged symmetrically on opposite sides of the galaxy.
F Superluminal motion.
F High rotational velocities near the nucleus.
F A bright, compact object at the very center.
F Luminosity 10-1000 times that of a normal galaxy.
F A giant sucking sound.
F All of above.
F None of above.
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AST 102 Practice Exam #2
Spring 2000
Sizes of white dwarfs and neutron stars
6
1x10
White dwarf
5
1x10
4
1x10
3
1x10
Neutron star
2
1x10
10
1
0.1
1
Mass (M )
10
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AST 102 Practice Exam #2
Spring 2000
Useful equations
Length contraction, time dilation and velocity
addition:
V2
∆x1 = ∆x2 1 − 2
c
∆t 2
∆t 1 =
V2
1− 2
c
v +V
v1 = 2
vV
1 + 22
c
Absolute interval =
∆x12 − c 2 ∆t 12 = ∆x22 − c 2 ∆t 22
Schwarzschild singularity (event
horizon):
CS =
or
∆t 1 =
1
∆x12 − ∆x22 + c 2 ∆t 22
c
∆x1 = ∆x22 − c 2 ∆t 22 + c 2 ∆t 12
c2
c 2CS
4πG
Mass-energy equivalence:
E = mc 2
Doppler effect:
λ − λ0 V
=
c
λ0
= ∆x 2 − c 2 ∆t 2
Useful rearrangements of the Absolute Interval
formula:
M=
4πGM
or
or
F
H
I
K
F λ − 1IJ
V = cG
H λ0 K
λ = λ0 1 +
V
c
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AST 102 Practice Exam #2
Spring 2000
How big is that?
Diameter of hydrogen atom
Diameter of the Moon
Diameter of the Earth
Diameter of the Sun
Diameter of the Milky Way
galaxy
Distance to the Moon
Distance to the Sun
Distance to the next nearest star
Distance to the center of the
Milky Way
Distance to the nearest galaxy
1.06×10-8 cm
3.5×103 km
1.3×104 km
1.4×106 km
1.7×105 ly
Typical lengths:
Normal star diameter
Distance between stars
Normal galaxy diameter
Distance between galaxies
106 km
a few ly
105 ly
106 ly
3.8×105 km
1.5×108 km
4 ly
2.7×104 ly
Typical masses:
Smallest star
Normal star
Giant star
Normal galaxy
Galaxy cluster
0.1 M
1 M
10 M
1010-1011 M
1014-1015 M
Mass of hydrogen atom
Mass of the Moon
Mass of the Earth
Mass of the Sun
1.67×10-24 gm
7.4×1025 gm
6.0×1027 gm
2.0×1033 gm
(1 M)
Mass of the Milky Way galaxy
5×1010 M
Typical luminosities:
Normal star
Giant star
Normal galaxy
Quasar
1 L
103-105 L
109-1010 L
1012-1013 L
Luminosity of the Sun
3.8×1033 erg/s
(1 L)
105 L
1010 L
Typical timespans:
Planetary revolution
Galaxy rotation
Life of giant stars
Life of normal star
1 year
107-109 years
106-109 years
1010 years
Typical speeds:
Planetary orbits
Stellar motion in galaxy
Between nearby galaxies
10 km/s
100 km/s
100 km/s
Luminosity of the largest stars
Luminosity of the Milky Way
galaxy
Luminosity of quasar 3C 273
Earth’s rotation period
Moon’s revolution period
Earth’s revolution period
Sun’s revolution period within
Milky Way
Age of the solar system
Expected life span of the Sun
Age of the Universe
Earth’s equator rotation speed
Earth’s revolution speed
Sun’s speed within the Milky
Way
Milky Way’s speed within the
local Universe
1.7×105 ly
1012 L
8.64×104 s
(1 day)
28 days
365.25 days
(1 year)
2.4×108 years
4.6×109 years
1.5×1010 years
1.3×1010 years
0.47 km/s
30 km/s
220 km/s
500 km/s
Other important constants:
1 ly = 9.46×1012 km = 9.46×1017
cm
1 km = 105 cm
1 hour = 3600 seconds
1 year = 3.16×107 seconds
π = 3.14159265359
1 Mly = 106 ly
1 erg = 1 gm
cm2/s2
Speed of light: c = 2.99792458×105 km/s =
2.99792458×1010 cm/s = 1 ly/year
Newton’s gravitational constant: G = 6.67×10-8
cm3/(gm s2)
Hubble’s constant: H0 = 20 km/(sec Mly)