TEST BANK 21ST CENTURY ASTRONOMY THE SOLAR SYSTEM 5TH EDITION BY KAY
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Chapter 18: Relativity
and Black Holes
Learning
Objectives.
Define the bold-faced vocabulary terms within the chapter.
18.1 Relative Motion Affects Measured
Velocities
Illustrate why relative motion causes two people to report
different observations of the same physical situation.
Multiple Choice: 1, 2, 4, 5, 7
Differentiate between the relative motion of a material
object and light as seen by two different observers.
Multiple Choice: 3, 6, 8
Short Answer: 1, 2
18.2 Special Relativity Explains How Time
and Space Are Related
Explain how traveling at relativistic speeds affects
measurements of time, length, speed, and energy.
Short Answer: 4, 5, 7, 9, 10, 12
Describe observational tests of special relativity.
Multiple Choice: 22, 26
Short Answer: 6, 11
Illustrate why relativistic space travel is highly
improbable.
Multiple Choice: 17, 18
Short Answer: 3, 8
18.3 Gravity Is a Distortion of Spacetime
Explain why “free fall is the same as free float.”
Multiple Choice: 45
Short Answer: 22
Illustrate how motion along a curved surface mimics motion in
a gravitational field.
Multiple Choice: 36, 42, 44
Short Answer: 16, 23
Illustrate how gravity is really motion of particles through
spacetime that has been curved by mass.
Multiple Choice: 35, 37, 47
Short Answer: 17, 19, 21
Describe observable consequences of general relativity.
Multiple Choice: 38, 39, 40, 43, 46, 48, 49, 50, 51, 52, 53
Short Answer: 15, 20
Describe observational tests of general relativity.
Short Answer: 18
Compare and contrast the accuracy of Newtonian vs.
relativistic physics.
Multiple Choice: 34, 41
Short Answer: 14
18.4 Black Holes
Explain the significance of the Schwarzschild radius (or
event horizon) of a black hole.
Multiple Choice: 54, 55, 60, 67
Short Answer: 25, 29, 30
Calculate the Schwarzschild radius of a black hole.
Multiple Choice: 56, 58, 59, 62, 66, 68, 69, 70
Assess whether an object is or is not likely to evolve into a
black hole.
Short Answer: 27
Describe why a black hole cannot be observed directly but how
it can be detected indirectly.
Multiple Choice: 57, 61, 63, 65
Short Answer: 24, 26
Summarize the observational evidence that black holes exist.
Multiple Choice: 64
Short Answer: 28
Working It Out 18.1
Calculate the relativistic effect of time dilation when
moving at high speeds.
Multiple Choice: 9, 10, 11, 12, 13
Working It Out 18.2
Calculate the masses of two stars in a binary system.
Short Answer: 13
MULTIPLE CHOICE
1.
What is the meaning of
the phrase inertial frame of reference?
a.
a reference frame that
is not accelerating
b.
a reference frame that
is stationary with respect to the Earth
c.
a reference frame that
is in motion at constant speed
d.
a reference frame that
is accelerating at a constant rate
e.
a reference frame in
which there are strong gravitational forces
2.
What will observers in
different inertial frames of reference always agree on?
a.
how the speed of light
varies with the motion of an observer
b.
the length of the
meter, but not the duration of the second
c.
the rate each frame is
accelerating
d.
the laws of physics
e.
whether events are
simultaneous or not
3.
Suppose that an object
is moving and it is emitting light toward you, in vacuum. What would you notice
about the light you observe?
a.
The wavelength gets
longer.
b.
The frequency gets
lower.
c.
The energy becomes
lower.
d.
The speed stays
constant.
e.
The speed is
increasing.
4.
You are driving on an
interstate at 70 mi/h and, in the adjacent lane in the same direction, another
car is passing you. From your point of view, the other car seems to advance at
10 mi/h, i.e., it is only slowly moving ahead of you. What is the speed that
the odometer should indicate inside the other car?
a.
70 mi/h
b.
10 mi/h
c.
80 mi/h
d.
60 mi/h
e.
75 mi/h
5.
You are driving on an
interstate at 70 mph and in the adjacent lane, but in the opposite direction,
another car is zipping by. From your point of view, the other car seems to pass
at 150 mph, which would seem crazy. What is the speed that the odometer should
indicate inside the other car?
a.
80 mph
b.
55 mpg
c.
220 mph
d.
110 mph
e.
150 mph
6.
You observe a distant
galaxy apparently moving away at one third the speed of light 
. If you could measure the speed at which
this galaxy’s light is passing the Earth, you would get
. If you could measure the speed at which
this galaxy’s light is passing the Earth, you would get
a.
b.
2 
c.
c.
d.
4 
e.
5 
7.
Stellar aberration
should be distinguished from stellar parallax in that
a.
stellar aberration
immediately allows for measurements of distances to stars.
b.
stellar parallax is
easily observable, whereas the aberration is impossible to measure.
c.
stellar aberration
depends on the Earth’s orbital speed around the Sun.
d.
stellar parallax
depends on the Earth’s orbital speed around the Sun.
e.
stellar aberration
demonstrates that the speed of light is infinite.
8.
Superluminal motions
were detected in jets of plasma launched by actively accreting compact objects.
This shows that
a.
special relativity has
a limited range of applications.
b.
observed superluminal
motions can be explained without violating the theory of relativity.
c.
black holes can
actually launch material jets that advance faster than light.
d.
general relativity
allows for faster-than-light motions, even though special relativity does not.
e.
the jets are aligned
with our line of sight, therefore we understand that their light is coming at
us faster than c speed.
9.
What is the Lorentz
factor for an object moving at 0.85c?
a.
1.00
b.
1.67
c.
1.89
d.
0.99
e.
2.05
10.
At what fraction of the
speed of light would the γ factor lead to a
10-fold time dilation?
a.
0.5
b.
0.95
c.
0.75
d.
0.995
e.
0.9999995
11.
If the Lorentz factor
is 2, what is the corresponding speed?
a.
0.86c
b.
1.55c
c.
0.27c
d.
0.52c
e. 0.9999c
12.
The second marked by a
clock aboard a fast (hypothetical) interstellar ship moving at v = 0.95c would be __________________
compared with the second marked by a clock at rest on Earth.
a.
70.71 times shorter
b.
70.71 times longer
c.
7.09 times shorter
d.
3.20 times longer
e.
3.20 times shorter
13.
A fast-moving muon
decays in 2 × 10−4 seconds, as
measured by an observer at rest. In the reference frame of the muon itself, its
lifetime is in fact only 2 × 10−6 seconds. What is
the muon's speed?
a.
0.05c
b.
0.50c
c.
0.95c
d.
0.995c
e.
0.99995c
14.
One consequence of
Einstein’s ideas about the speed of light is that
a.
if two events take
place at the same time for one observer, they will occur simultaneously for all
observers.
b.
whether events are seen
as simultaneous or not depends on the motions of observers.
c.
two events cannot
happen at the same time for two different observers.
d.
it is not possible to
know when an event happens.
e.
people could design and
fly interstellar spaceships moving as fast as light itself.
15.
What is the meaning of
the word spacetime?
a.
It is a mental
framework for keeping track of numbers in Newtonian physics.
b.
Space and time form a
two-dimensional region where physics takes place.
c.
The term has no special
meaning; it’s just a fancy way to sound important when talking about physics.
d.
It is the combined
treatment of space and time in the theory of relativity.
e.
It is the idea that
observers will always measure the same locations and times of events.
16.
According to Einstein’s
Theory of Special Relativity, which two quantities are different manifestations
of the same thing?
a.
mass and gravity
b.
light and energy
c.
energy and mass
d.
temperature and energy
e.
distance and time
17.
According to Special
Relativity, spacecraft that would travel faster than the speed of light are
a.
impossible, because
nothing can travel that fast.
b.
possible, but not
useful since they could not contain living beings.
c.
impossible, since
objects that travel that fast would get shorter and squeeze out space for the
astronauts to live.
d.
possible, if we are
clever enough with new technologies.
e.
impossible, because
they would require new energy sources that are not yet invented.
18.
Why can an object with
a nonzero mass never travel as fast as the speed of light?
a.
It would take an
infinite amount of energy to accelerate it to a speed of c.
b.
It would emit so much
radiation that its energy would decrease and it would slow down again.
c.
It would lose all its
mass and turn into neutrinos.
d.
An object can actually
travel as fast as light, but if it did it would disappear.
e.
If it were going at the
speed of light, it would be converted to pure energy since E = mc2.
19.
In an accelerator, a
massive particle may gain a relativistic speed for which its total energy is
1,000 time greater than its rest energy. This implies a Lorentz factor of
a.
0.999.
b.
10.
c.
1.
d.
1000.
e.
2.29.
20.
At what (relativistic)
speed does the length of a spacecraft become half of its rest length?
a.
0.40c
b.
0.27c
c.
0.99c
d.
0.87c
e.
0.10c
21.
What is true about
muons?
a.
They are always moving
at high speed, so they test relativity.
b.
Relativity explains why
we can see muons that are produced high in the atmosphere from cosmic rays.
c.
We can see them being
deflected from straight lines by the gravity of black holes.
d.
They have a mass that
does not increase if they are moving fast.
e.
They are examples of
Hawking radiation from black holes.
22.
Has relatively ever
been tested?
a.
No, because it would
require us to set up physics experiments in faraway galaxies.
b.
Yes, because even
ordinary motion in automobiles and airplanes produces easily noticeable effects
predicted by relativity.
c.
No, because no one has
been able to think of experiments that are able to measure the small
differences between the predictions of Newtonian physics and relativity.
d.
Yes, because (for
example) subatomic particles can be accelerated to speeds approaching that of
light.
e.
No, because the theory
of relativity contains paradoxes and contradictions, like the twin paradox.
23.
Which of the following
is a consequence of Einstein’s Special Theory of Relativity?
a.
Moving clocks run
quicker.
b.
The velocity of light
depends on the speed of the observer.
c.
Distances are shorter
for objects traveling close to the speed of light.
d.
Gravity arises because
mass distorts spacetime.
e.
Faster moving objects
require less force to accelerate them.
24.
The twin paradox shows
that special relativity
a.
explains many things
but can’t explain everything.
b.
is accurate but
contains some worrisome contradictions.
c.
is incorrect.
d.
is incomplete.
e.
correctly accounts for
the results of experiments in different reference frames.
25.
Which of the following
statements is not valid?
a.
If the speed of light
is finite, time must run differently for different observers.
b.
The results of physics
experiments are indistinguishable in inertial frames and freely falling frames.
c.
The high positional
accuracy provided by the GPS system is possible if relativistic corrections are
applied.
d.
Time is contracted and
distances dilated in moving frames.
e.
If the speed of light
is finite, telescopes could be seen as “time machines.”
26.
The Large Hadron
Collider at CERN in Switzerland can accelerate protons to amazing kinetic
energies of the order of 1.6 × 10−7J. What would be
the Lorentz factor for a proton of mass 1.67 × 10−27 kg at such speed?
a.
133
b.
1065
c.
70.79
d.
2
e.
999
27.
For a fast
(hypothetical) interstellar ship moving at v = 0.95c a distance of 10 ly between neighboring stars would
actually measure
a.
32 ly.
b.
10.5 ly.
c.
3.1 ly.
d.
9.5 ly.
e.
10 ly.
28.
In Special Relativity
the total energy of a fast moving object (kinetic plus rest energy) is given by
E = γmc2, where m
is the rest mass of the object. At what (relativistic) speed would the kinetic energy of a 100-ton spaceship be the same as its rest energy?
a.
1c
b.
0.999c
c.
0.5c
d.
0.25c
e.
0.87c
29.
Of all four muons
produced at 15 km above ground and schematically shown in the figure below,
which one would “see” the distance to the ground as a mere 200 m?
a.
the muon moving at 0.9c
b.
the muon moving at 0.99c
c.
the muon moving at
0.999c
d.
the muon moving at
0.9999c
e.
the muons would not
experience any relativistic effect because they are too tiny.
30.
Assume that a group of
explorers traveled to the Orion Nebula, which is the nearest star-forming cloud
and is at a distance of 1,300 light-years, using revolutionary technology that
allowed them to travel at a speed of 0.99c. Observers
back on Earth using Earth-bound clocks would say it took the explorers
__________ to get there, but the explorers with their moving clocks would say
it took them only __________ to get there.
a.
1,310 years; 185 years
b.
1,440 years; 630 years
c.
1,310 years; 390 years
d.
1,440 years; 425 years
e.
1,310 years; 1,300
years
31.
If you were to design a
spacecraft that could travel to the galactic center fast enough that the
astronauts aboard aged by only 25 years during the trip, how fast would the
spacecraft have to go? (Note: The galactic center is 25,000 light years away.)
a.
0.95c
b.
0.995c
c.
0.99995c
d.
0.9999995c
e.
0.999999995c
32.
Suppose you detect a
pulsar that gives us 1,000 radio pulses per second, but the pulsar is in a
distant galaxy that is apparently moving away from us at 50 percent of the
speed of light. An observer at rest with respect to the pulsar in that faraway
galaxy would measure a pulse rate of
a.
870 per second.
b.
1,150 per second.
c.
1,250 per second.
d.
1,366 per second.
e.
1,450 per second.
33.
The satellites from the
GPS network are in high orbits and their clocks fall behind ground-based clocks
by about 7 µs/day. Assuming that this dilation is entirely a special
relativistic effect, which is the best estimate for the orbital speed of a GPS
satellite?
a.
27,500 km/h
b.
14,000 km/h
c.
1,000 km/h
d.
67,000 km/h
e.
38,500 km/h
34.
When do the predictions
of Special Relativity match those of Newtonian physics?
a.
in terrestrial laboratories
b.
inside our Solar System
c.
when different
observers are at rest with each other
d.
when objects have a low
mass
e.
when objects are moving
slowly
35.
__________ is the
result of mass distorting the fabric of spacetime.
a.
Energy
b.
Radiation
c.
Fusion
d.
Gravity
e.
Electric charge
36.
What does gravity mean
in relativity?
a.
It is a result of mass
and energy being two forms of the same thing.
b.
It is a consequence of
distances getting shorter as objects move faster.
c.
It is the result of the
mass of falling bodies getting bigger because they are in motion.
d.
It is the force that
objects with mass exert on a body.
e.
It is the result of the
distortion in spacetime around an object with any energy density.
37.
A geodesic is
the name for the
a.
aberration of
starlight.
b.
gravitational field of
the Earth.
c.
solid crust of a
terrestrial planet.
d.
path followed by a
freely falling object in spacetime.
e.
shape of a body that
has mass.
38.
Gravitational lensing
occurs when _____________ distorts the fabric of spacetime.
a.
a star
b.
dark matter
c.
a black hole
d.
any massive object
e.
a white dwarf
39.
The bending of light
paths near a massive object is the essence of
a.
time dilation.
b.
the twin paradox.
c.
gravitational lensing.
d.
length contraction.
e.
mass increase.
40.
General relativity
predicts that coalescing (merging) massive objects would trigger
a.
pulses of
electromagnetic radiation.
b.
gravitational waves.
c.
high-energy particles.
d.
a slowing of clocks
here on the Earth.
e.
blueshifted light from
the surface of the object.
41.
How does relativity
compare with Newtonian physics?
a.
Relativity gives the
same result as Newtonian physics when objects are moving slowly.
b.
Relativity gives
results that contradict many predictions of Newtonian physics, so we know the
latter is incorrect.
c.
Relativity must be
better, because it is a newer theory than Newtonian physics.
d.
Newtonian physics and
relativity make the same predictions, but it’s easier to compute results using
relativity.
e.
Newtonian physics is
well accepted by scientists, whereas relativity is still controversial.
42.
You measure that an
object has a mass of exactly 1 kg. The Equivalence Principle says that the mass
you would measure by trying to accelerate it would be
a.
1 kg.
b.
greater than 1 kg.
c.
less than 1 kg.
d.
different from 1kg,
depending on what it’s made of.
e.
larger than 1 kg,
because of the Sun’s gravity.
43.
Photons have no mass,
and Einstein’s theory of general relativity says
a.
their paths through
spacetime are curved in the presence of a massive body.
b.
their apparent speeds
depend on the observer’s frame of reference.
c.
they should not be
attracted to a massive object.
d.
their wavelengths must
remain the same as they travel through spacetime.
e.
their wavelengths would
grow longer as they travel through empty space.
44.
The Equivalence
Principle says that
a.
the universe is
homogeneous and isotropic.
b.
being stationary in a
gravitational field is the same as being in an accelerated reference frame.
c.
at any radius inside a
star the outward gas pressure must balance the weight of the material on top.
d.
mass and energy are
interchangeable and neither can be destroyed.
e.
gravity does not exist
in space.
.
45.
Why do astronauts in
space feel no gravity?
a.
There is no gravity out
in space.
b.
Gravity happens only
when objects are accelerating.
c.
In space, the gravity
from the Moon and the Sun cancels out the Earth’s gravity.
d.
They and their
spaceship are both freely falling at the same rate in the gravitational field.
e.
The astronauts do not
have any mass when they are out in space.
46.
The Principle of
Equivalence states that the gravitational mass is equal to the
a.
mass when moving nearly
the speed of light.
b.
resistance to acceleration.
c.
mass when near a black
hole.
d.
weight of the object.
e.
density divided by the
volume.
47.
In the rubber-sheet
analogy for spacetime, what would you expect for objects (such as golf balls)
rolling around in the presence of a massive object that is stretching the
rubber sheet?
a.
Their paths will be
straight if they are moving slowly enough.
b.
Their paths will curve
more the closer they come to the massive object.
c.
Their paths will curve
by the same amount no matter how close they come to the mass.
d.
Their paths will curve
toward the mass if they pass close but bend away from the mass if they pass far
from the mass.
e.
Their paths will curve
less the closer they come to the massive object.
48.
The gravitational
redshift of light should be smallest for light emitted from the surface of
a.
a black hole.
b.
the Sun.
c.
a white dwarf.
d.
a planet like the
Earth.
e.
a neutron star.
49.
According to the theory
of relativity, a clock on top of Mount Everest would run ___________ compared
with a clock at sea level because ______________ .
a.
faster; of the high
altitude, which means a slightly weaker gravity
b.
faster; the air is a
lot thinner and there is less friction within the clock
c.
faster; it is closer to
the Moon and thus experiences stronger tide forces
d.
slower; of the low
pressure at that altitude
e.
identically; time is
the same for all clocks in the universe
50.
The Sun’s mass would
affect the spacetime in its proximal space and photons from distant stars would
follow curved geodesics rather than straight paths when passing close to our
star, as in the figure shown below. According to general relativity, an
observer on Earth would also expect the “apparent stars” to appear
a.
redder.
b.
hotter.
c.
more distant.
d.
bluer.
e.
more massive.
51.
Which of the following
applications (which affects many people) could not have been achieved without
implementing necessary relativistic effects and corrections?
a.
fast-moving automobiles
b.
GPS technology
c.
interstellar travel
d.
radar technology
e.
neutrino detectors
52.
Compared with a clock
on the surface of the Earth, a clock on the International Space Station runs
a.
at approximately the
same rate, but slightly slower.
b.
significantly slower.
c.
significantly faster.
d.
sometimes faster and
sometimes slower.
e.
at an equal rate,
except during eclipses.
53.
Light is increasingly
redshifted near a black hole because
a.
the photons are moving
away from us very quickly as they are sucked into the black hole.
b.
the photons are moving
increasingly faster in order to escape the pull of the black hole.
c.
the photons lose energy
because climbing out of the black hole’s gravity makes them weaker.
d.
the curvature of
spacetime is increasingly stretched near the black hole, which in turn
stretches the wavelengths of the photons.
e.
time is moving
increasingly slower as viewed from the observer’s frame of reference.
54.
The event horizon of a
black hole is defined as
a.
the point of maximum
gravity.
b.
the radius of the
original neutron star before it became a black hole.
c.
the radius from which
shock waves course through spacetime due to the strong gravitational distortion
of the black hole.
d.
the radius at which the
escape speed from the black hole equals the speed of light.
e.
the radius at which the
gravitational force is the same as that on the surface of the Sun.
55.
What is the
significance of the Schwarzschild radius around a black hole?
a.
It is the radius at
which an orbiting object would show a precession.
b.
It is the radius at
which gravitational redshift can be detected.
c.
It is the radius at
which the black hole’s spin equals the speed of light.
d.
It is the radius at
which the escape velocity equals the speed of light.
e.
It is the radius at
which a body falling onto the black hole would move at half the speed of light.
56.
The Schwarzschild
radius of a 10 M⊙ is
__________ the size of the Schwarzschild radius of a 5 M⊙ black hole.
a.
b.
c.
equal to
d.
2 times
e.
5 times
57.
Hawking radiation from
black holes refers to
a.
light emitted from
matter falling onto a black hole.
b.
the gravitational
redshift of light emitted near the event horizon.
c.
the radiation of
particles created near the event horizon.
d.
high-energy X-rays and
gamma rays from the formation of a black hole.
e.
the optical and
infrared light from an energetic supernova explosion.
58.
If the Sun suddenly
turned into a black hole, what would be the radius of its event horizon?
a.
3 m
b.
30 m
c.
300 m
d.
3 km
e.
30 km
59.
If the Earth were to
shrink in size until it became a black hole, its Schwarzschild radius would be
a.
1 cm.
b.
1 m.
c.
1 km.
d.
10 km.
e.
200 km.
60.
A person would
experience __________ as he or she approached the event horizon of a black
hole.
a.
extremely strong tidal
forces
b.
intense heating
c.
strong Hawking radiation
d.
strong infrared
radiation
e.
nothing
61.
Hawking radiation is
emitted by a black hole when
a.
the black hole rotates
quickly.
b.
the black hole accretes
material.
c.
a supernova explodes
and forms a black hole out of its core.
d.
synchrotron radiation
is emitted by infalling charged particles.
e.
a virtual pair of
particles is created near the event horizon.
62.
If the Sun were to be
instantly replaced by a 1 M⊙ black
hole, the gravitational pull of the black hole on Earth would be
a.
much greater than it is
now.
b.
the same as it is now.
c.
much smaller than it is
now.
d.
larger or smaller,
depending on the location of the Moon.
e.
irrelevant, because
Earth would quickly fall into the Sun and be destroyed.
63.
Even if a black hole
emitted no light, we can still detect it
a.
from sound waves produced
by material falling onto the black hole.
b.
by tides produced on
the Earth’s oceans.
c.
through its Hawking
radiation.
d.
through its
gravitational effect on surrounding gas or stars.
e.
by looking for dark
patches on the sky where the black hole swallows background light.
64.
A red giant star is
found to be orbiting an unseen object with a short orbital period. By measuring
the speed at which it orbits, astronomers deduce that the unseen object has a
mass of 10 M⊙. This
object is probably a ______________ because ________________.
a.
black hole; the giant
star is massive and could be in orbit only about something even more massive
b.
black hole; its mass is
too large to be a neutron star or a white dwarf
c.
neutron star; any
supernova that would have made a black hole would have destroyed the red giant
d.
M-dwarf star; only such
stars would be faint enough to go unseen in this system
e.
black hole; most red
giants orbit neutron stars, and neutron stars can turn into black holes
65.
Black holes that are
stellar remnants can be found by searching for
a.
dark regions at the
centers of galaxies.
b.
variable X-ray sources.
c.
extremely luminous
infrared objects.
d.
objects that emit very
faint radio emission.
e.
regular, repeated
pulsations at radio wavelengths.
66.
What black-hole mass
would have an event horizon radius comparable to the size of an atomic nucleus?
a.
100 kg
b.
1011
kg
c.
100 tons
d.
1024
kg
e.
0.1 kg
67.
Which of the following
are the only possible properties of black holes?
a.
mass, angular momentum,
and electrical charge
b.
mass, electrical
charge, and fraction of heavy nuclei
c.
electrical charge,
density, and dark matter content
d.
angular momentum, mass,
and elasticity
e.
mass, density of dark
matter, and temperature of Hawking radiation
68.
While traveling through
the galaxy in a spacecraft, you and a colleague set out to investigate the 106
M⊙ black
hole at the center of our galaxy. He hops aboard an escape pod and drops into a
circular orbit around the black hole, maintaining a distance of 10,000 km,
while you remain much farther away in the spacecraft. After doing some
experiments to measure the strength of gravity, your colleague signals his
results back to you by using a green laser. What would you see? Hint: You will
need to calculate the location of the event horizon.
a.
You would see your
colleague’s signals unaltered in wavelength, because he is orbiting well
outside the event horizon of the black hole.
b.
You would see your
colleague’s signals shifted to a much redder wavelength, because he is close to
the event horizon.
c.
You would never get to
see the escape pod carrying your colleague reaching the desired orbit; thus,
you’d never get any signals back from him.
d.
You would see nothing,
because no light can escape the gravitational pull of a black hole no matter
how far your colleague is from it.
e.
You would see your
colleague’s signals shifted to a much bluer wavelength, because black holes can
make highly energetic light.
69.
While traveling through
the galaxy in a spacecraft, you and a colleague set out to investigate the 106 M⊙ black
hole at the center of our galaxy. She hops aboard an escape pod and drops into
a circular orbit around the black hole, maintaining a distance of 1 AU, while
you remain much farther away in the spacecraft. After doing some experiments to
measure the strength of gravity, your colleague signals her results back to you
by using a green laser. What would you see? Hint: You will need to calculate
the location of the event horizon.
a.
Your colleague’s
signals are shifted only slightly toward the red, because she is orbiting well
outside the event horizon of the black hole.
b.
You would see your
colleague’s signals shifted to a much redder wavelength, because she is close
to the event horizon.
c.
You would see nothing,
because your colleague has crossed the event horizon around the black hole.
d.
You would see nothing,
because no light can escape the gravitational pull of a black hole no matter
how far your colleague is from it.
e.
You would see your
colleague’s signals shifted to a much bluer wavelength, because black holes can
make highly energetic light.
70.
While traveling through
the galaxy in a spacecraft, you and a colleague set out to investigate the 106 M⊙ black
hole at the center of our galaxy. She hops aboard an escape pod and drops into
a circular orbit around the black hole, maintaining a distance of 4 ×
106 km, while you remain much farther
away in the spacecraft. After doing some experiments to measure the strength of
gravity, your colleague signals her results back to you by using a green laser.
What would you see? Hint: You will need to calculate the location of the event
horizon.
a.
You would see your
colleague’s signals unaltered in wavelength, because she is orbiting well
outside the event horizon of the black hole.
b.
You would see your
colleague’s signals shifted to a much redder wavelength, because she is close
to the event horizon.
c.
You would see nothing,
because your colleague has crossed the event horizon around the black hole.
d.
You would see nothing,
because no light can escape the gravitational pull of a black hole no matter
how far your colleague is from it.
e.
You would see your
colleague’s signals shifted to a much bluer wavelength, because black holes can
make highly energetic light.
SHORT ANSWER
1.
Explain, in the context
of the special relativity, how a telescope is a kind of “time machine.”
2.
Let’s assume we know
that the semi-major axis of the “loop” described by a star’s position due to
stellar aberration is equal to the orbital speed of the Earth (expressed in
units of light speed c in vacuum). What would be the corresponding
angular opening of the cone in the figure below?
3.
Give a simple
explanation to why the speed cannot increase as suggested by the Newtonian
behavior shown as a straight line in the figure below.
4.
What is the central
idea in relativity concerning the speed of light? Describe at least two unusual
consequences of this idea.
5.
Explain what
four-dimensional spacetime means.
6.
What is the meaning of
the equation E = mc2?
7.
Explain why no object
that has mass can ever move at a speed equal to the speed of light. At what
velocity do massless particles (e.g., photons) travel in vacuum?
8.
Use the figure shown
below to explain that the implied acceleration has indeed a value close to the
accepted value for the acceleration of Earth’s gravity.
9.
Suppose we discovered
radio signals coming from the star Alpha Centauri, which is 4.4 light-years
from us, and we sent a crew in a spacecraft to visit it. If the spacecraft used
revolutionary technology allowing it to travel at a speed of 0.5c, how long would it take the spacecraft to get to Alpha
Centauri, and how much time would the astronauts say passed during the trip?
(Ignore the time it would take to accelerate the spacecraft to reach a velocity
of 0.5c.)
10.
Explain the
relativistic effects on clocks aboard the International Space Station compared
with synchronized clocks here on Earth.
11.
Muons are elementary
particles that decay into other particles in about 2.2 microseconds. They are
formed in the upper atmosphere of the Earth from high-energy cosmic rays and
can be detected on the ground even though they could travel only a few hundred
meters before decaying, according to Newtonian physics. How does relativity
explain that we can detect them on the ground? Explain both in our reference
frame and in the frame of the muon.
12.
The GPS system requires
time accuracy of the order of a few tens of nanoseconds (ns) for the clocks
aboard the satellites. At the high altitudes where the satellites are deployed,
their orbital speeds are about 20,000 km/h. Based on arguments Special
Relativity alone show that time dilation corrections are absolutely relevant
and necessary in order to maintain the aforementioned accuracy level.
13.
A 15-M⊙ star has been monitored for decades and scientists found
that it is orbiting in a highly eccentric ellipse about an unseen mass
(presumably a supermassive black hole [BH]) at the center of Milky Way with a
period of 15.6 years and a semimajor axis of about 1000 A.U. What is the mass
of the unseen object?
14.
Explain how Newtonian
physics is an approximation to relativity.
15.
What are gravitational
waves? Have they been detected?
16.
How would the Newtonian
theory explain the orbit of the Earth around the Sun? What would the
explanation be in general relativity?
17.
What is the “rubber
sheet” analogy for spacetime, and why is it useful for explaining gravity and
gravitational waves?
18.
Describe two early
classical tests of the general relativity.
19.
Explain why Einstein’s
theory of general relativity predicts the existence of gravitational lensing.
20.
How might we be able to
detect events like colliding neutron stars even if we don’t detect any light
from them?
21.
Explain how mass and
compactness would play into affecting the way an object distorts the fabric of
spacetime.
22.
What is the Equivalence
Principle? Describe a consequence of the equivalence principle for astronauts
orbiting in the space station.
23.
Galileo supposedly
experimented with gravity by dropping two objects of different masses from the
Leaning Tower of Pisa at the same instant and observing that they hit the
ground at the same time. If Albert Einstein had done the experiment, how would
his conclusion have differed from Galileo’s?
24.
What does singularity mean in the context of black holes?
25.
What is the difference
between the singularity and the event horizon of a black hole?
26.
Explain why Hawking
radiation may not be a practical way to observe black holes.
27.
Describe two possible
ways to make a stellar-size black hole.
28.
You repeatedly measure
the radial velocity of what seems to be a single main-sequence star like the
Sun but find that it in fact is in a tight orbit around another object that
remains unseen. From measurement of the velocity and orbital period, you
calculate that the unseen object has a mass 20 times that of the Sun-like star.
Why might this object be a black hole?
29.
Roughly estimate the
magnitude of the tidal acceleration between the feet and the head of an
astronaut when he is approaching a 1 M⊙ black hole (BH) and is
100 km from it, as in the figure shown below. Compare that acceleration with
the standard acceleration of gravity here on Earth. Would “spaghettification”
be a good way to describe the effect on the human being?
30.
Based the line of reasoning
you (hopefully) outlined in the previous problem, would it be more likely for
an astronaut to be subject of “spaghettification” when 100 km away from the
event horizon of a supermassive BH of 100 million solar masses or when 100 km
away from the event horizon of a 1 solar mass BH?
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