ASTR 1290: Final Practice Quizzes
Rank the following parts of the electromagnetic spectrum for shortest wavelength to longest wavelength. gamma rays infrared visible light radio ultraviolet X-rays
gamma rays < X-rays < ultraviolet < visible light < infrared < radio Review slides from lecture 6.
Why is the Penrose process astrophysically important? a. It demonstrates that the rotational energy of a black hole can be tapped by matter outside the event horizon. b. It demonstrates how black holes gain mass and angular momentum via accretion. c. It shows that the mass of a black hole can only decrease and never increase. d. It shows that an observer in the ergosphere can observe an object with negative rest mass energy.
A A is correct. As we shall see later in the class, something like the Penrose process can occurs when magnetic fields are present in the matter falling into the black hole. B is incorrect because the black hole loses mass and angular momentum in the Penrose process. C is wrong because the mass does decrease. D is wrong because a local observer always infers a positive energy for an object.
Kelly and Michael are astronauts on a mission to Mars. Kelly is exploring the planets surface while Michael orbits at 8 Martian radii in their spacecraft's command module. Each astronaut carries a very accurate atomic clock with them for their missions. What do they perceive about each other's clock? a. Michael thinks that Kelly's clock runs slow while Kelly thinks that Michael's clock runs fast. b. Kelly thinks that Michael's clock runs slow while Michael thinks that Kelly's clock runs fast. c. They both think the other's clock runs slow. d. They both think the other's clock runs fast.
A A is correct. Since Kelly is deeper in the gravitational potential of the planet, her clock does run slow relative to Michael's. Since Kelly thinks here clock runs normal, she perceives that Michael's clock is fast. Remember this is unlike time dilation in special relativity, where both observer's think the other's clock is slow.
What makes white dwarf supernovae useful to astronomers? a. They are all thought to have approximately the same luminosity so they can be used measure distances to very distant galaxies. b. Their light curves are very consistent and can be used as accurate clocks. c. They are much brighter than massive star supernovae and can be used to locate distant galaxies. d. Modeling of their light curves provides a precise test of general relativity
A A is correct. The primary use of white dwarfs is to measure distances to very distant galaxies. This method was used to infer that the expansion of the universe is accelerating.
Why do we think most pulsars begin with rapid spins (spins periods less than a second)? a. As the star's radius decreases, any small rotation is amplified via conservation of angular momentum. b. The star that forms the pulsar accretes lots of matter from a companion that makes it very rapidly spinning. c. The electromagnetic radiation carries away negative angular momentum that acts to spin up the star. d. Most pulsars don't begin with rapid spins - they must be spun up by accretion.
A A is correct. This is just like how a skater pulls her arms into increase her rotation rate. In the case of part B, it is not thought that the star that produces the neutron star is rapidly spinning. Electromagnetic radiation carries away positive angular momentum so C is false. D is incorrect because most pulsars are thought to be born rapidly spinning. This is true of most young pulsars that we observe.
Why is black hole a better term than frozen star? a. Black hole accounts for the infinite redshift effect making light from the event horizon unobservable. b. Frozen implies the black hole is very cold when it is actually very hot. c. Black hole emphasizes that the concept of spacetime breaks down at the event horizon. d. Frozen star is a bad term because black holes have nothing to do with stars.
A A is the only correct statement. As discussed in class, black holes are black because they are infinite redshift surfaces. This make any light emitted near the event horizon unobservable. B is a poor choice because the freezing is "real" from the standpoint of an observer far from the black hole. If it were not for the infinite redshift, we would see the collapsing star and anything that fell in after "frozen" at the event horizon. Spacetime does not break down at the event horizon and black holes are thought to form from gravitational collapse of stars.
Gravity's effect on light is best described by which of the following statements? a. Gravity bends the path of light just like it bends the path of a massive object. b. Gravity has no effect on the path of light because light is made up of massless particles (photons). c. General relativity predicts that gravity could bend light but the effect is too small to yet measure so it is only hypothetical. d. The bending of light by gravity is forbidden because the speed of light is constant.
A A is the only correct statement. Light is bent by gravity and the effect is quite easy to observer with modern astronomical instrumentation. Light from distant galaxies is frequently bent by galaxies along our line of sight to these background galaxies.
In relativity, two observers share the same frame of reference only if a. they are not moving relative to each other. b. they are both located in the same place and are stationary. c. they agree on the laws of nature. d. they are both located in the same place regardless of motion. e. they are both located in the same place and are traveling at the same speed.
A As discussed in lecture 7, reference frames are defined in terms of relative motion. The position of an observer plays no role in defining the frame. Observers have the same reference frame if and only if they have the same velocity.
In 2018, NASA's Solar Probe Plus is expected become the fastest man made object ever, reaching velocities of 200 km/s. By what factor γ will clocks seem to run slow at this velocity? a. 1.0000002 b. 1.0003 c. 1.02 d. 2.1 e. 3.5
A Clocks run slow by the Lorentz factor γ. To compute γ, we first compute v/c = (200 km/s)/(300,000 km/s) = 0.00067. Then we use the formula γ = 1/√(1-(v/c)²) to find γ = 1.0000002. Remember, time dilation only becomes large when velocities get very close to the speed of light.
Donald and Daisy are moving at constant velocity in their space ships. Suppose Donald is moving away from Daisy at 85 km/h. Donald throws a ball in Daisy's direction at a speed of 75 km/hr. According to Daisy, which of the following is going on? a. She sees him moving away from her at 85 km/hr and the ball moving away from her at 10 km/hr. b. She sees him moving towards her at 85 km/hr and the ball moving toward her at 75 km/hr. c. She see him moving away from her at 85 km/hr and the ball moving towards her at 75 km/hr. d. She sees him moving away from her at 85 km/hr and the ball moving toward her at 10 km/hr.
A From Daisy's point of view, Donal is moving away at 85 km/hr. Since the ball is moving at -75 km/hr from Donald, addition of velocities yields 10 km/hr from Daisy's point of view.
The gravity of the Earth is exerting a force on a man standing on the ground. Which of the following statements is implied by Newton's 3rd law? a. The gravitational force of the man on the Earth is equal and opposite to the gravitational force of the Earth on the man. b. The normal force of the ground on the man is equal and opposite to the gravitational force of the Earth on the man. c. The net force on the man must be zero because he is not being accelerated. d. The gravitational force on the man must be balanced by some equal and opposite force on the man.
A Newton's 3rd law deals with action - reaction pairs. It is important to remember that the forces in this pair act on different objects. Both b and d deal with two forces that are acting on the man so they do not represent action -- reaction pairs. Statement c deals with Newton's 2nd law. So, a is the only correct response.
An absorption line is observed in the lab to be at 1000 nm. If a star moves perpendicular to our line-of-sight at 1/1000 of the speed of light, what is the observed wavelength of the absorption line from this star? a. 1000 nm b. 1001 nm c. 1010 nm d. 990 nm e. 999 nm
A Since the star is moving perpendicular to our line of sight, we do not see a Doppler shift. Doppler shift requires the star to be moving towards or away from us.
Cosmic rays are particles in space that travel very close to the speed of light. Some cosmic rays are inferred to have Lorentz factors of γ = 10⁶ (or even much higher). The Milky Way galaxy is about 100,000 light-years across meaning that it takes about 100,000 years for the cosmic ray to travel this distance from the point of view of a static observer. In the frame moving with the cosmic ray, how much time passes as it covers this distance? a. About a month b. About a day c. About a year d. About 10 years e. About 100,000 years
A Time dilation says that the passage of time in the frame of the cosmic ray is shorter by a factor γ = 10⁶. Since 100,000 year equals 10⁵ years, we find the time in the cosmic ray frame to be 10⁵ years/10⁶=0.1 years or about a month.
Examples of a freely falling observer include: a. An astronaut in orbit around the Earth. b. A skydiver who has just jumped out of an airplane. c. A man standing in an elevator that is going down at normal speed. d. A man standing in an elevator that is going up at normal speed. Ignore air resistance and choose all that apply.
A and B A is not a freely falling observer because gravity is not acting. D and E are not freely falling because the man is standing in the elevator so he is being supported against gravity by the normal force exerted by the floor of the elevator. Both B and C are freely falling observers if air resistance is negligible. B is a freely falling observer because orbit corresponds to falling with gravity at just the right rate to maintain circular (or elliptical) motion.
Which of the following are statements of one of Newton's laws of motion? a. For any force, there is always an equal and opposite reaction force. b. The square of an object's orbital period is proportional to the cube of the object's semi-major axis. c. An object moves with constant velocity if no net force is acting upon it. d. The acceleration of an object is inversely proportional to the net force acting upon it. e. The energy of an object is conserved. Choose all that apply.
A and C Both a and c express ideas that are restatements of Newton's laws of motion. Statement b deals with Newton's law of gravitation -- not motion. Statement d is close to one of Newton's laws, but states the wrong relation: acceleration is proportional to the net force -- not inversely proportional. Newton's law to not explicitly address energy conservation.
Rank these people by their gravitational potential energy relative to Earth from lowest to highest. (Remember to set the < signs when doing the ranking.) A woman flying in an airplane A woman standing on the ground a sea level A woman in deep space, far from Earth A woman in low Earth orbit
A woman standing on the ground a sea level < A woman flying in an airplane < A woman in low Earth orbit < A woman in deep space, far from Earth We could use the formulat PE = -GMm/r. Since r is the only thing changing, we can see that potential energy will increase (become less negative) as r increases. Or we make an analogy with the roller coaster, where the furthe from the Earth (higher), the more gravitational potential energy that you have. So, the correct order is: woman at sea level, woman in airplane, woman in low Earth orbit, and woman in deep space far from Earth.
Einstein's Field Equations state that the source of spacetime curvature can include: a. mass b. pressure c. electric fields d. magnetic fields Choose all that apply.
A, B, C, and D Mass and energy are closely related in special relativity. General relativity extends this relationship so that almost any type of energy can act as a source gravity. Since all of the above are associated with energy, they all act as a source of gravity. Since gravity is caused by spacetime curvature in GR, they are all sources of spacetime curvature.
Why were isolated neutron stars expected to be difficult to see in the early 1960s? a. They cool very rapidly. b. Before they cool, they have very small emitting area so they are dim. c. Before they cool, they have a very small flux so they are dim. d. We need space based telescopes to view X-rays and sensitive X-ray instruments had not yet been launched into space. e. The light from their surface is nearly infinitely redshifted. Choose all that apply.
A, B, and D A, B, and D are correct. Neutrons stars do cool rapidly due their large flux and there is not source of energy (e.g. no fusion) to replenish the lost energy. The emitting are is small due to their very small radii. C is incorrect because neutron star fluxes are huge due to the high initial temperatures - a trillion times larger than the Sun's flux. D is true. The first X-ray instruments were launched on rockets in 1962 but they were not sensitive enough to see the dim isolated neutron stars. E the redshift is large compared to normal stars but still less than a factor of a few so this is false.
Choose all of the following items that are accelerating. a. A car moving on a curved road at a steady 50 km/hr b. A car moving on a straight road at a steady 100 km/hr c. A golf ball at the peak of its flight through the air d. A rock falling off a cliff
A, C, and D
In 1905, Albert Einstein published papers describing which of the following phenomenon? a. theory of special relativity b. theory of general relativity c. the photoelectric effect d. proof of the wave nature of light e. theory of the random motion of particles Select all that apply.
A, C, and E The wave nature of light had long been demonstrated. Einstein did not publish work on the theory of general relativity until several years later.
In the late 1800's, most physicists believed that light travelled through a hypothetical medium called the aether because a. they thought the speed of light was much smaller than it actually is. b. they believed light was a wave and all other examples of waves travelled through some medium. c. Michelson and Morley had incorrectly claimed that they had measured the variation of light's velocity relative to the aether. d. Newton had incorrectly postulated the existence of the aether and everyone assumed Newton was correct because of his success explaining the laws of motion and gravity.
B
Why was it important that the apparatus in the Michelson and Morley experiment could rotate? a. Rotation allowed them to compensate for the Earth's rotation b. They were looking for a change in the signal as the paths from the mirrors to the beam splitter change orientation relative to the Earth's motion through the aether. d. They needed rotation to change the path lengths between the mirrors and the beam splitter. e. Rotation was required because the detector needed to be rotating relative to the beam splitter.
B
Why are some physicists still searching for theories of gravity that are alternatives to general relativity? a. There are small but significant discrepancies between existing tests of general relativity and the predictions of the theory. b. The observed acceleration of the universe is not consistent with the predictions of general relativity unless we invoke the existence of some unknown "dark energy". c. The theory of general relativity can explain existing tests but is not mathematically self-consistent. d. Observations of the motion of galaxies in clusters of galaxies indicate that gravity is much weaker than expected given the amount of mass that is observed in these galaxies.
B A is incorrect because general relativity is consistent with all existing precision tests. C is incorrect because the theory is mathematically self-consistent. D sounds sort of like the evidence for dark matter, but remember that the gravitational force appears to be stronger than expected from the observed matter, driving the need for additional dark matter. B is correct because the universe is observed to be accelerating and this is inconsistent with general relativity unless we posit the existence of some very strange unknown field that physicists call dark energy. This leads some physicists to consider alternative theories of gravity.
Which of the following statements is correct? a. More massive stars live longer lives and are more luminous. b. More massive stars live shorter lives and are more luminous. c. More massive stars live longer lives and are less luminous. d. More massive stars live shorter lives and are less luminous.
B B is correct. More massive stars are more luminous. Since the luminosity goes up very rapidly with increasing mass, they use up their greater energy budget (E=mc^2) in much less time, leading to shorter lifetimes.
If you free fall feet first into a black hole, what do you see as you cross the event horizon? a. You see light from above and below you blue-shifted and light from your sides is redshifted. b. You see light from above and below you redshifted and light from your sides is blue-shifted. c. You see the whole history of the universe, but with an extreme blueshift. d. Everything has its normal color, although it is lensed by the black hole.
B B is correct. The tidal gravity redshifts the light from things above and below you, but blue-shifts light coming from the side. You don't see the whole history of the universe unless you can stop on the horizon, which is impossible. Light is lensed by the black hole but it is also blue-shifted and redshifted depending on the direction.
What causes stars to form? a. Interstellar gas is compressed by the motion of nearby stars. b. Interstellar gas collects and collapses under its mutual gravitational attraction c. Stars start off as planets that grow by accreting interstellar gas. d. Stars form primarily from the collision of other stars.
B B is the only correct statement. See the first few slides of lecture 21.
Imagine you live on a planet orbiting a billion solar mass Schwarzschild black hole at many 1000s of Schwarzschild radii. You are an astronaut assigned to a space station orbiting at the black hole's innermost stable circular orbit. Your sister stays on the planet. In the time it takes you to age one year, how much does your sister age? (Hint: For simplicity, ignore your orbital motion and assume you are static.) a. year b. 1.2 years c. 3 years d. 30 years e. An infinite number of years
B For practical purposes, we can treat the planet as being at infinity. The innermost stable circular orbit (ISCO) is at 3 Rₛ, so we compute the redshift factor z = √((1-Rₛ)/(3-Rₛ) = √(2/3). The factor by which your sister thinks your clock runs slow is the inverse of this: √(2/3) = 1.22. Hence, your sister ages about 1.2 year for every year you age. Note that the redshift factor we use is only correct for a static observer at the ISCO. If we accounted for your orbital motion, the answer would be slightly different.
What does frame dragging in general relativity imply for satellites orbiting the Earth? a. Their orbits are unstable. b. Their orbits experience a small precession. c. Their orbits must be prograde. d. Their orbits experience a large (easily measurable) precession.
B Frame dragging will cause orbits to precess. The precession due to frame dragging (Lens-Thirring precession) is a small effect for the Earth. Orbits also precess for other reasons (Earth's varying gravitational field due asphericity, other general relativistic effects) so it is difficult to isolate the effect due to frame dragging. Since frame dragging is a weak effect for Earth, retrograde orbits are not prohibited.
Which of the following does special relativity say inertial observers must agree on? a. the order of events at different locations. b. the observer's relative speed c. the observer's lengths d. the time between events
B In special relativity, observers must agree on their relative speed. All of the other quantities listed are dependent on the observer's reference frame.
Our galaxy is filled with clouds of molecular gas which is can be quite cold compared to stars. If this gas has a temperature of 80 K, in what part of the spectrum will its emission peak? (Hint: a figure of the electromagnetic spectrum with wavelength ranges in meters can be found in lecture 6: Properties of Light .pdf on the collab site.) a. Radio b. Infrared c. Visible d. Ultraviolet e. X-rays
B Inserting 80K in to Wien's laws yields 2.9 x 10⁶/80 = 3.6 x 10⁴ nm. If we look at the electromagnetic spectrum, it is given in meters so we multiply by 10⁹ to convert nanometers to meters to get 3.6 x 10⁻⁵ m, which lies in the infrared.
What is the size of the Schwarzschild radius for a black hole with the mass of the Earth (6 x 10²⁴ kg)? a. 9 micrometers b. 9 millimeters c. 9 meters d. 9 kilometers
B Plugging in to the formula Rₛ = 2GM/c² with specified mass yields about 9 mm.
Mary-Kate is an astronaut who leaves Earth to travel at a large fraction of the speed of light to a nearby star and then returns to Earth. During the trip, 25 years pass for her twin Ashley on Earth, but Mary-Kate is only 4 years older upon her return. How can this aging difference be reconciled with the concept that different inertial observers in relative motion each perceive the other observer's clock to run slow? a. It cannot be reconciled. This scenario is not allowed by special relativity. b. Special relativity does not apply because Mary-Kate is not an inertial observer during this trip. c. Special relativity only says that inertial observers in relative d. motion perceive each other's clocks to run slow. It does not e. require their clocks to run slowly by the same amount. f. Special relativity does not apply when the velocities are close to the speed of light.
B Special relativity only applies to observers in inertial reference frames. Mary-Kate experiences large accelerations during her trip: first when she leaves Earth, then when she arrives at her destination, again when she leaves her destination, and then finally when she returns to Earth. These accelerations mean that she is not an inertial observer and account for the difference between her and Ashley.
Mary-Kate is an astronaut who leaves Earth to travel at a large fraction of the speed of light to a nearby star and then returns to Earth. During the trip, 25 years pass for her twin Ashley on Earth, but Mary-Kate is only 4 years older upon her return. How can this aging difference be reconciled with the concept that different inertial observers in relative motion each perceive the other observer's clock to run slow? a. It cannot be reconciled. This scenario is not allowed by special relativity. b. Special relativity does not apply because Mary-Kate is not an inertial observer during this trip. c. Special relativity only says that inertial observers in relative motion perceive each other's clocks to run slow. It does not require their clocks to run slowly by the same amount. d. Special relativity does not apply when the velocities are close to the speed of light.
B Special relativity only applies to observers in inertial reference frames. Mary-Kate experiences large accelerations during her trip: first when she leaves Earth, then when she arrives at her destination, again when she leaves her destination, and then finally when she returns to Earth. These accelerations mean that she is not an inertial observer and account for the difference between her and Ashley.
Why do black hole event horizons appear to be black for observers far away? a. The outward moving light gets slowed by gravity and falls back into the hole b. The event horizon is a surface of infinite redshift c. The event horizon is a surface of infinite blueshift d. The event horizon has no matter so it cannot emit light
B The event horizon of a black hole primarily appears black because it is an infinite redshift surface. If this were not the case, observers far from the black hole would see everything that ever fell into the black hole "frozen" on the event horizon.
Why don't physicists understand much about the nature of the singularity? a. The assumptions underlying the theory of general relativity break down at the event horizon of the black hole. b. General relativity breaks down in regions of infinite curvature and we have no complete theory of quantum gravity. c. The interior of black holes is probably five dimensional space while general relativity assumes four dimensions. d. Real black holes probably do not have singularities because that formed from a collapsing star.
B The only correct statement is that general relativity breaks down in regions of infinite curvature. We think we need a quantum theory of gravity to describe spacetime in this limit. We have no reason to believe that black hole interiors are five dimensional. General relativity predicts that singularities do form from stellar collapse. There is nothing special about the event horizon in this context - general relativity should work fine there.
Assume Jupiter's orbit is circular (a good approximation). If Jupiters orbital speed is 13 km/s and its orbital radius is 7.78×10¹¹m, what is Jupiter's orbital acceleration? a. 1.67×10⁻⁸m/s² b. 2.17×10⁻⁴m/s² c. 2.17×10⁻²m/s² d. 1.67×10⁻⁴m/s²
B We compute the acceleration using the formula for circular motion a = v²/r. To get consistent units we need to convert km/s to m/s. Since there are 1000 m in a km, we have 13 km/s = 13,000 m/s. Then we can compute a = (1.3 x 10⁴ m/s)²/(7.78 x 10¹¹)=2.17 x 10⁻⁴ m/s².
Why do astronomers want to build the Thirty Meter Telescope on the summit of Mauna Kea? a. It is one of the best sites in the southern hemisphere for astronomical observing b. It is one of the best sites in the northern hemisphere for astronomical observing c. It is the best site other than the Canary Islands but they can't build it in the Canary Islands due to local opposition there. d. It is the best site other than Chile but they can't build it in the Chile due to local opposition there.
B is correct because Mauna Kea is one of the best sites in the Northern (not Southern) Hemisphere and possibly the absolute best. Any other potentially comparable sites are too undeveloped or remote to utilize at this time. Many sites in Chile are actually better than Hawaii, but Europe is already building the ELT in Chile and astronomers would prefer to have large telescopes in both the northern and southern hemisphere. There is not significant opposition to building new telescopes in Chile.
Which of the following are true about white dwarfs supported by degeneracy pressure? a. Their radius increases as their mass increases b. Their radius decreases as their mass increases c. They have a theoretical maximum mass of 1.4 solar masses d. They are the densest stars in the universe that are not black holes e. Our sun will eventually become a white dwarf Choose all that apply.
B, C, and E Stars supported by degeneracy pressure have radii that decrease when their mass increases so A is incorrect and B is correct. The theoretical maximum mass of white dwarfs (Chandrasekhar mass) is 1.4 solar masses so C is correct. D is incorrect because neutron stars are denser than white dwarfs. E is correct -- the Sun will eventually become a white dwarf.
Human body temperature is 37 degrees C. Convert this to K (look it up!) and find the corresponding value in K. What wavelength does this correspond to? a. 94,000 nm b. 78,000 nm c. 9,400 nm d. 7,800 nm e. 940 nm f. 780 nm
C 37 C corresponds to 310 K (we add 273 to convert C to K). Plugging this into Wien's law yields about 9400 nm. This is in the infrared part of the spectrum.
When it was first developed, what known anomaly could the theory of general relativity explain that Newtonian gravity could not? a. A displacement in angular position of background stars when observed close to the Sun. b. The observed rate of increase in distance between the Earth and the Moon. c. The rate of precession of the perihelion of Mercury. d. The variation in the speed of light with direction relative to Earth's motion.
C A, B, and C all represent tests of general relativity, but only C was a known issue when Einstein started working on relativity. A was a prediction of the theory that was later confirmed and the precise measurement of the distance between Earth and Moon didn't occur until after the Apollo missions. So C is the correct answer.
Given that we observe stars from the surface of the Earth, do we observe stars to appear exactly the same as an observer freely floating out in deep space would? a. Yes. There is nothing special about our place in the universe. b. No. Since we are on the Earth's surface, the light from distant stars is redshifted by a very small amount by the time it reaches us. c. No. Since we are on the Earth's surface, the light from distant stars is blue-shifted by a very small amount by the time it reaches us. d. Yes. The light could be blue-shifted or redshifted, but the equivalence principles says it is by the same amount for us as the observer out in space.
C All light coming towards Earth from very far away experiences a very small blueshift. In contrast, radiation coming from the surface of the Earth appears redshifted to observers far from Earth. D is incorrect because a freely floating observer in space is not equivalent to a static observer in a gravitational field on Earth.
If you reach the event horizon of a black hole, what happens afterward? a. You are trapped in the black hole but can move around freely. b. You are trapped forever at the event horizon of the black hole. c. You are inevitably pulled into the singularity. d. You enter a parallel universe.
C All matter and light crossing the event horizon ends up in the singularity. Space "falls" faster into the singularity than anything, even light can travel.
Why are accreting black holes thought to form jets? a. The jets are associated with the emission of Hawking radiation from the black hole's event horizon. b. Accreting black holes are not thought to form jets. This phenomenon only occurs for accreting neutron stars. c. Magnetic fields threading the accretion disk or black hole are wound up by rotation, which accelerates particles that then radiate. d. The jets are thought to form because of the relativistic beaming of light emitted on the approaching side of the accretion disk.
C C is correct. Almost all theoretical models of jets attribute them to magnetic fields. Magnetic fields which are rotating at their base get wound up into a helical pattern. This helical structure collimates charge particles into a narrow structure while accelerating them and causing them to radiate.
What is the main reason that pulsars spin down? a. They are spun down by accretion. b. Due to a Penrose like process in their ergospheres, just like black holes. c. They are spun down by an electromagnetic wind. d. Most pulsars generally spin up and only rarely spin down.
C C is correct. Pulsars predominantly spin down via an electromagnetic wind. Accretion tends to spin pulsars up rather than down. Pulsars due have a frame dragging effect on the spacetime around them but it is too small for a Penrose like process to work. Pulsars in accreting systems due appear to be spun up, but these are a small minority of cases.
Tina and Amy are astronauts headed on an interstellar mission to Proxima B. To escape the pull of the Sun's gravity, they are accelerating in their spacecraft at a constant rate. Amy is stationed at the front of the rocket while Tina is near the back. How does Tina's atomic clock compare to Amy's atomic clock? a. Both clocks must agree because they are traveling with the same velocity. b. Tina's clock appears to run faster than Amy's clock because it is accelerating in the direction of Amy's clock. c. Amy's clock appears to run faster than Tina's clock because it is accelerating in the direction away from of Tina's clock. d. Both clocks seem to run slow.
C C is correct. Remember that being in an accelerating frame is equivalent to being in a gravitational field, with being closer to the front of the spacecraft being analogous to being higher in the gravitational potential and being near the back like being deeper in the gravitational potential. Hence Tina's clock runs slower than Amy's clock. See lecture 14 and the pdf notes on collab for more discussion.
Why are there usually two high tides per day at any location on the Earth? a. The tidal bulges are both toward and opposite the Moon's location and these bulges move across the Earth as the Moon orbits the Earth. b. The tidal bulge that points toward the Moon's location rotates twice as fast as the Earth. c. The tidal bulges are both toward and opposite the Moon's location, and move relative to the surface as Earth rotates. d. One high tide is caused by the Moon's gravity and a second high tide is caused by the Sun's gravity.
C C is correct. There are two bulges along direction from Moon's center to the Earth's center - one is on the side facing the Moon and the other is on the opposite side of the Earth. These bulges move relative to the Earth's surface because of the Earth's rotation and the Moon's orbit. However, the reason there are two per day is because of the Earth's rotation. The variation in the timing of the tides due to the Moon's orbit is a smaller effect that varies a month timescale. The tidal bulges due to the Sun are somewhat smaller than the Moon and lead to more moderate annual variations in the tides.
What makes pulsars so useful to astronomers? a. They are very bright and all have the same luminosity so we can use them to measure distances to other galaxies. b. The absorption lines in their spectra allow us to make sensitive tests of general relativity in regions of strong gravity. c. Their large inertia and rapid spins make their pulses very precise clocks. d. We can measure their ages very accurately, putting lower limits on the age of the universe.
C C is the only correct statement. Pulsar do make very precise clocks. Pulsars are not particularly bright and we do not think they all have the same luminosity. Pulsars have no atomic features in their radio emission. Those that we can see in the X-ray also do not have features in their X-ray spectrum. We can not accurately measure the ages of pulsars. They can infer ages from spin down but these are not particularly reliable.
Grass looks green because a. it emits green light and absorbs other colors. b. it absorbs green light and emits other colors. c. it reflects green light and absorbs other colors. d. it transmits green light and emits other colors.
C Grass emits its own light, but only in the infrared where we can see it. The light we do see is the reflected light. Grass appears green because it predominantly reflects green light.
Which of the following motivated Kepler to develop his laws of planetary motion? a. He wanted to show that Brahe's measurements were incorrect. b. He wanted to prove that Copernicus was wrong about the Sun being the center of the solar system. c. He believed that the motion of heavenly bodies should obey simple mathematical laws. d. He wanted to prove that Newton's law of universal gravity was correct.
C Kepler did believe that heavenly bodies should obey simple relations so c is correct. Kepler may have wanted to disprove Brahe's model, but he knew that Brahe's measurements were the most accurate and precise available and used them to derive his laws. Kepler favored the heliocentric model so he agreed with Copernicus. Newton was not yet living when Kepler formulated his laws.
Special relativity tells us that a. Different observers must agree on the order in which all events occur. b. Different observers must always agree on the order in which all events happen, but can disagree on whether they happen at the exact same time. c. Different observers must agree on the order events happen if the events occur in the same location. d. Different observers can disagree on the order of events even when the events are causally connected.
C Observers must always agree on the order of events that are causally connected. This is always applicable to events that occur at the same location and sometimes true of events that occur at different locations but are sufficiently close together in time. However, observers do not need to agree on the order of events that are not causally connected. This means that c is true but a, b and d are not true.
The first calculations of stellar collapse to form a black hole were carried out in 1939, but most physicists were skeptical. By the early 1960s, many more physicists had come around to the idea that black holes might actually happen in nature. What changed? a. They started seeing clear observational evidence of black holes. b. The discovery of pulsars showed that neutron stars existed, lending weight to the earlier work which predicted their existence. c. Computers had advanced to the stage that one could compute the collapse with realistic physical models for pressure and thermodynamics d. All of the above.
C Only C is true. In the early 1960s, clear evidence of black holes did not exist and neutron stars were not discovered until 1967. So, the main breakthrough in the early 60s was theoretical rather than observational. Computers had advanced significantly due to the strong motivation and large amounts of funding provided by the development of nuclear weapons.
How is peer review used by scientists? a. Peer review is used to determined whether articles reporting research results should be published in scientific journals. b. Peer review is used to prioritize which research proposals should receive federal funding. c. Both A and B. d. Neither A nor B.
C Peer review is used by scientists in two primary ways. To determine whether articles reporting scientific results should be published in scientific journals and to prioritize which research proposals should be given federal funding.
A star made entirely of neutrons could have a radius of 10km and mass equal to the Sun's mass (2 x 10³⁰ kg)? What would its escape velocity be (assuming Newtonian gravity is correct)? a. 1/100th the speed of light b. 1/10th the speed of light c. ½ the speed of light d. slightly greater than the speed of light e. much larger than the speed of light
C Plugging the numbers into the formula of escape velocity vₑₛ𝒸 = √(2GM/R) yields a value v = 1.6 x 10⁸ m/s whereas the speed of light is about 3 x 10⁸ m/s so this corresponds to about half the speed of light. So, a star made of neutrons would probably be close to forming a black hole but not quite a black hole.
Which of the following examples describes a situation where a car is experiencing a net force? a. The car is moving at constant velocity. b. The car is stopped on a hill. c. The car is making a gradual turn. d. The car is stopped on a level pavement.
C Remember an object has a net force when the sum of all forces acting on it down cancel. Newton's first law says that any object experiencing a net force has an acceleration so we can identify cases that are accelerating. Cases a, b, and d are not experiencing an acceleration so they do not have a net force. In c there is an acceleration so there is a net force.
What is the meaning of the statement that black holes have "no hair"? a. Black holes must be spherically symmetric b. Black holes cannot have an electric charge c. All properties of black holes can be specified if you know their mass, charge, and angular momentum d. Most properties of black holes can be specified if you know their mass, charge, and angular momentum
C The "no-hair" theorem is a statement that the Kerr-Newman metric is the most general black hole solution in general relativity. In this solution all (not just some) properties of the spacetime are determined by just three quantities: the mass, angular momentum, and charge.
Once an accretion disk forms, how does matter lose angular momentum in order to slowly move towards the black hole? a. The matter does not need to lose angular momentum to move inwards. b. The viscosity caused by collisions between particles provides friction between neighboring rings in the disk. c. The turbulent magnetic fields provide friction between neighboring rings in the disk. d. The radiation forces from light emitted by the accretion disk provide friction between neighboring rings in the disk.
C The correct answer is C. Matter that is in a disk is rotating so it has angular momentum and must lose angular momentum to move toward smaller radii. Simulations show that magnetic turbulence generated by the magnetorotational instability allow matter to accrete on to the black hole. Both particle collision and radiation forces due provides some friction, but both are very small compared to the effects of magnetic turbulence.
The equivalence principle implies that: a. Freely falling in a gravitational field is equivalent to being accelerated in a rocket. b. Being static in a gravitational field is equivalent to floating freely in space where gravity is negligible. c. Freely falling in a gravitational field is equivalent to floating freely in space where gravity is negligible. d. Energy is equivalent to mass times the speed of light squared.
C The equivalence principle is a statement about the relationship between freely falling frames and frames where acceleration is zero. It says that an observer who is freely falling in a gravitational field doesn't "feel" her own gravity. She would experience weightlessness just as if she were floating in space without any acceleration. A good example of this is an astronaut in orbit around the Earth.
From which objects' surface would the gravitational redshift of light be largest for an observer very far away? a. The Earth with M=6 x 10²⁴ kg and R=6400 km b. The Sun with M=2 x 10³⁰ kg and R=7 x 10⁵ km c. A white dwarf star with M=2 x 10³⁰ kg and R=6400 km d. A red giant star with M= 2 x 10³⁰ and R=3 x 10⁸ km
C The gravitational redshift goes like GM/(rc²). Since G and c are constants this means that redshift is proportional to M/r. The mass is the same for B, C, and D, so the object with the largest redshift is the one with the smallest radius, which is the white dwarf. Since the white dwarf star and the Earth have the same radius, but the white dwarfs mass is nearly a million times larger, it must have the largest redshift. So the answer is C.
You and a highway patrolman are driving at constant speeds in opposite directions on a straight highway. The patrolman is driving at 60 mph and his radar gun determines your relative speed (the magnitude of the difference between your velocities) to be 135 mph. What is your speed at the time of measurement? a. 60 mph b. 135 mph c. 75 mph d. 185 mph
C The magnitude of the difference between your velocities is 135 mph, but you are traveling in opposite directions so this corresponds to -135 mph relative to the patrolman's direction of travel. Adding -135 mph to 60 mph gives -75 mph. The fact that this is negative makes sense because you are traveling in the opposite direction. Your speed is the magnitude of this velocity or 75 mph.
Why is Newton's version of Kepler's third law so useful to astronomers? a. It tells us that all planetary orbits are elliptical b. It allows us to calculate distances to objects c. It allows us to calculate masses of distant objects d. It allows us to calculate the rotation rates of stars
C This was discussed in lecture 5.
Which object has the most kinetic energy? a. a 4-ton truck moving 50 km/hr b. a 3-ton truck moving 70 km/hr c. a 2-ton truck moving 90 km/hr d. a 1-ton truck moving 110 km/hr e. A, B, C, and D all have the same energy
C We need to use the KE=0.5Mv² formula to evaluate the options. In this case, it is not necessary to change units because all examples are given with the same units. 4 * 502 = 10000, 3 * 702 = 14700, 2 * 902 = 16200, 1 * 1102 = 12100. Since 16200, is largest, the answer is c.
What makes the concept of a four dimensional spacetime useful for understanding relativity? a. One can treat transformations between the coordinate systems carried by different observers as analogous to rotations of coordinate systems in three dimensional space. b. The theory of general relativity treats gravity as arising from spacetime curvature. c. Observers do not have to agree on the properties of space alone or properties of time alone, but they do have to agree on the properties of spacetime. d. All of the above e. Only A and C.
D
If you have a 75 watt light bulb, how much energy does it use each minute? a. 75 joules b. 450 joules c. 4500 watts d. 4500 joules e. 450 watts
D A minute corresponds to 60s and a watt is a joule/second so we need to multiply 60s by 75 watts to obtain 4500 joules. Remember that joules is the unit of energy -- not watts which measures energy per unit time (or power).
Rose and Dimitri are traveling on trains passing each other in exactly opposite directions, both traveling at constant velocity. Which of the following is true? a. Rose and Dimitri agree on the length of her train car along the direction of travel. b. Rose and Dimitri agree on the time between events. c. Rose and Dimitri agree on which events are simultaneous. d. Rose and Dimitri agree on the width of her train car perpendicular to direction of travel.
D A, B, and C are all observer dependent quantities in special relativity. In contrast, length contraction only applies for lengths along the direction of travel. Lengths perpendicular to the direction of motion are measured to be the same by two observers.
The acceleration of gravity on Earth is approximately 10 m/s² (9.8 m/s²). If you drop a bowling ball off a cliff, how fast will it be falling after 4 seconds? a. 400 m/s² b. 400 m/s c. 40 m/s² d. 40 m/s e. 4 m/s f. 4 m/s²
D Acceleration is the rate of change is velocity. So assuming the rock starts from rest (you drop it), we have vf = at = (10m/s²) (4s) = 40 m/s so the answer is d. Pay attention to units.
Which of the following statements about the maximum mass of neutron stars is true? a. The maximum mass is not thought to be much bigger than 3 solar masses b. We know that the maximum mass is greater than 2 solar masses from observations c. The precise value of the maximum mass is unknown due to our limited understanding of the strong force. d. All of the above are true e. Only A and B are true.
D All of these statements are true. See the lecture 24 slides for a discussion of all of these points.
Can a particle that has mass (equal to m) ever reach the speed of light? a. Yes. You just need to give it an amount of energy equal to mc². b. Yes, but it will require a much larger amount of energy than mc². c. No, because a massive particle traveling at the speed of light would have energy equal to 0.5mc² which is more than its rest mass energy. d. No, because a massive particle traveling at the speed of light would have infinite energy and would therefore require an infinite amount of energy to accelerate.
D Answer D is correct. As v gets closer to c, the g factor continues to increase, eventually becoming infinite at v=c. Since energy is proportional to g, it also must be infinite. Hence infinite energy must be provided to the particle, but we believe the energy of the universe must be bounded (less than infinity).
A leading candidate for dark matter are weakly interactive massive particles (WIMPs) -- the idea that our galaxy is filled with such particles which are difficult to detect but have mass and contribute to the galaxy's gravity. One way of detecting these particles is via their interaction with Xenon. Where do scientists place such experiments? a. On satellites orbiting the Earth. b. On top of mountains. c. At sea level. d. In mines deep below the Earth's surface.
D As discussed in this week's blog reading, the experiments for liquid Xenon are done in mines deep below the Earth. They are placed deep below the Earth to eliminate other particles (for example cosmic rays) that might also interact with the Xenon but will be absorbed at the Earth's surface.
Rick and Ilsa are traveling rockets heading in opposite directions. As they fly by each other, they exert very small forces on each other to measure each other's mass and then compare these to measurements that were made when they were not moving relative to each other. (Since the forces are small, you can ignore non-inertial effects caused by their acceleration.) Which of the following are true? a. Rick thinks Ilsa's mass increased but she thinks his decreased when moving. b. Ilsa thinks Rick's mass increased but he thinks hers decreased when moving. c. Both find that the other's mass stayed the same when moving. d. Both think that the other's mass increased when moving. e. Both think that the other's mass decreased when moving.
D By now, it should be clear that special relativistic effects are symmetric so both observers see the same effect. Hence, neither A nor B could be correct. As discussed in lecture, moving masses increase relative to non-moving masses so D is correct.
If we increase the temperature of a star that emits like a blackbody by a factor of 2, what happens? a. Its flux goes up by a factor of 4 and its peak wavelength doubles b. Its flux goes up by a factor of 4 and its peak frequency doubles c. Its flux goes up by a factor of 16 and its peak wavelength doubles d. Its flux goes up by a factor of 16 and its peak frequency doubles
D D is correct. Flux goes at temperature to the fourth power and 2⁴ = 16. Wien's law says that if you double the temperature, you decrease the wavelength by a factor of 2. Since frequency is and wavelength of light are inversely related, that means that the frequency doubles.
How were the first neutron stars discovered? a. Radio astronomers were looking for thermal emission from neutron stars. b. Radio astronomers were looking for the radiation from electrons accelerated in the neutron star's strong magnetic field. c. Radio astronomers were looking for pulsating sources and the ones they found were eventually shown to be neutron stars. d. Radio astronomers were looking for other things and discovered sources that seemed to pulse by accident.
D D is correct. The discovery of neutrons stars was accidental. The graduate student who discovered them had a tough time convincing her senior colleagues that they were not from man made noise sources.
What will the gravity inside a black hole do to your body as you get closer to the singularity? (Assume you fall in feet first.) a. It will rip apart you body by stretching you in an extreme fashion. b. It will rip apart the individual cells in your body. c. It will rip apart your atoms into the individual protons, neutrons and electrons. d. All of the above e. Only A and B.
D D is correct. The tidal gravity forces continue to increase as you get closer to the singularity. At first, they merely rip you apart, but eventually they become so strong that the variation of the gravitational force across a nucleus is enough to break the nucleus apart.
Where are tidal forces due to gravity the largest? a. At the horizon of a billion solar mass black hole. b. Just inside the horizon of a billion solar mass black hole. c. At the horizon of a 10 solar mass black hole. d. Just inside the horizon of a 10 solar mass black hole.
D D is correct. Tidal forces increase as radius decreases and this continues inside the horizon with the largest tidal forces occurring near the singularity. The tidal forces due to a 10 solar mass black hole are actually much larger (by a factor of 100 million trillion) than those of a billion solar mass black hole.
What happens next after a star uses up all the hydrogen in its core? a. It starts fusing helium in its core and the star contracts. b. It starts fusing helium in its core and the star expands. c. It starts burning hydrogen in a shell and the star contracts. d. It starts burning hydrogen in a shell and the star expands.
D D is correct. When the hydrogen is used up, the core is still not hot and dense enough for helium fusion to proceed. It first goes through a phase where it fuses more hydrogen to helium in a shell around the core. During this stage the outer envelope of the core expands, making it a giant star. (Red giant for low mass stars and blue supergiant for higher mass stars.)
What primarily supports a main sequence star against gravity? a. Electron degeneracy pressure. b. Neutron degeneracy pressure. c. Gas pressure maintained by nuclear fission. d. Gas pressure maintained by nuclear fusion. e. Gas pressure maintained by gravitational contraction.
D Gas pressure is the main source of pressure support against gravity in a main sequence star.
A skinny physicist has been hitting the gym and lifting weights to try to increase his mass but he just can't manage to gain any. Knowing a little relativity, he decides to measure his mass in a spaceship traveling very close the speed of light. Does he see his mass increase? a. Yes. The mass of moving objects increases. b. No. The mass of objects is independent of their motion. c. No. The mass of moving objects decreases. d. No. From his standpoint, he is not moving so he measures the same mass as always.
D It is true that the mass of a moving object increases, but only from the standpoint of an observer in relative motion. From the physicists own standpoint in the spacecraft, he is not moving and the rest of the universe is moving by him. Hence, he observes no increase in his own mass.
In general relativity, which of the following paths corresponds to a geodesic? a. The path followed by freely falling objects. b. The path followed by light. c. The path followed by planets in orbit around the Sun. d. All of the above. e. Only A and C.
D Light and freely falling objects both follow paths called geodesics. Since planets in orbit are freely falling (accelerating under gravity), they also follow geodesics. So all three statements are correct.
A neutron star is a very dense type of star. The gravitational fields at the surface of a neutron star are almost a trillion times larger than on Earth. How would yellow light emitted from the surface of the neutron star appear to an observer very far from the star? a. It would experience a small blueshift. b. It would experience a large blueshift. c. It would experience a small redshift. d. It would experience a large redshift. e. It would be observed at the same wavelength of yellow light as it was emitted.
D Light deep in a gravitational potential appears to be redshifted to an observer who is farther out in the potential. Since the gravity of a neutron star is very large, the redshift is very large so D is the correct answer.
Assume that a star radiates as a thermal (blackbody) emitter. If we keep the luminosity of the star fixed but quadruple its radius, what would happen to its temperature? a. It will increase by a factor of 4 b. It will increase by a factor of 2 c. It will remain unchanged d. It will decrease by a factor of 2 e. It will decrease by a factor of 4
D Remember that L=FA and A=4piR² so if we quadruple R, we increase A by a factor of 16. Since luminosity stays fixed and A increases, the flux F must decrease by a factor of 16. Finally, we use the fact that F = sigma T⁴ to infer that if flux decreases by a factor of 16, then T must decrease by a factor 16^(1/4) or by a factor of 2.
Why were physicists not that worried about the large hadron collider (LHC) at CERN producing black holes that would destroy the Earth? a. They were certain that the LHC could not produce black holes. b. They were fairly certain that any black holes produced would evaporate before they could grow. c. Collisions of cosmic rays with the Earth's atmosphere routinely achieve the same energies so the threat of black holes from such collisions must be small or the Earth would have already been destroyed. d. Both B and C
D Reread the article from you blog assignment which discusses the risks: http://content.time.com/time/health/article/0,8599,1838947,00.html Scientists did believe the production of black holes was a remote possibility, but were excited that this might occur. They thought the threat to Earth was remote because Hawking radiation would cause the black holes to evaporate before they could accrete. Even if physicist were wrong about the evaporation, the energies achieved in the CERN collisions are also routinely achieved by cosmic rays hitting the Earth's atmosphere and we are still here. So both B and C are correct.
Cooper is an astronaut who leaves Earth to travel at a large fraction of the speed of light to a nearby star and then returns to Earth. During the trip, 76 years pass for Cooper's daughter, but Cooper is only a couple of years older upon his return. How can this aging difference be reconciled with the concept that different inertial observers in relative motion each perceive the other observer's clock to run slow? a. It cannot be reconciled. This scenario is not allowed by special relativity. b. Special relativity does not apply when the velocities are close to the speed of light. c. Special relativity only says that inertial observers in relative motion perceive each other's clocks to run slow. It does not require their clocks to run slowly by the same amount. d. Special relativity does not apply because Cooper is not an inertial observer during this trip.
D Special relativity only applies to observers in inertial reference frames. Cooper experiences large accelerations during his trip: first when he leaves Earth, then when he arrives at his destination, again when he leaves his destination, and then finally when he returns to Earth. These accelerations mean that he is not an inertial observer and account for the difference between him and his daughter.
What is the cosmic censorship hypothesis? a. We cannot know what happens inside an event horizon because no information (light) can leave the black hole. b. Singularities are forbidden from forming when a star collapses. c. Singularities come in pairs that must be separated by event horizons. d. Singularities are always hidden behind event horizons.
D The cosmic censorship hypothesis states that there are no naked singularities. That is, all singularities must be hidden behind event horizons.
The gravitational time dilation due to Earth's gravitational fields is best described as: a. A very small effect, which is so small that we cannot measure it. b. A very small effect, which we have only been able to measure in the last 10 years. c. A fairly large effect, but one which we do not notice because we don't move far from Earth's surface. d. A very small effect, but one that is essential to account for in the operation of the global positioning system (GPS).
D The gravitational time dilation effect at Earth's surface is small, but large enough that the clocks on orbiting satellites (that our far from Earth) must account for it if their clock are to stay synched with those on Earth's surface. Without correcting for relativity, GPS would be much less accurate because accurate clocks are need to measure light travel time from the satellite to the Earth's surface. So D is the correct answer.
Consider two observers. Sebastian is traveling in a spaceship at ½ the speed of light. Belle is traveling in another spaceship moving perpendicular to Sebastian's at ¼ the speed of light. What do Belle and Sebastian perceive about each other's clocks? a. Both perceive each other's clocks to agree because they are moving perpendicular to each other. b. Belle thinks that Sebastian's clock runs fast. c. Sebastian thinks that Belle's clock runs fast. d. Sebastian thinks that Belle's clock runs slow. e. Belle thinks that Sebastian's clock runs slow. Select all that apply.
D and E Both perceive the other to be moving relative to their frame of reference. Hence both perceive the other's clock to run slow. This conclusion is independent of the orientation of their velocities.
Anna and Etienne are traveling on trains passing each other in opposite directions, both traveling at constant velocity. Which of the following are true? a. Anna thinks that Etienne's train car is longer than Etienne does. b. Etienne thinks that Anna's train car is longer than Anna does. c. Anna and Etienne both agree on the length of their respective train cars. d. Anna thinks that Etienne's train car is shorter than Etienne does. e. Etienne thinks that Anna's train car is shorter than Anna does. Choose all that apply.
D and E Length contraction means that we always perceive moving objects to be shorter in their direction of travel than an observer who is moving with the object. Since Etienne sees Anna's train car moving, he must perceive it to be shorter than Anna, who moves with the car. Likewise, Anna sees Etienne's train car moving, so she must perceive it to be shorter than Etienne who is moving along with the car. Hence D and E are both true but A, B, and C are all incorrect.
Rank the following US federal funding agencies from highest to lowest in terms of how much funding they provide for astronomy and astrophysics research. (Remember to set the < signs when doing the ranking.) National Science Foundation National Aeronautics and Space Administration Department of Energy
Department of Energy < National Science Foundation < National Aeronautics and Space Administration
How does the light cone constrain your future? a. Your future must lie within the light cone. b. Regions of spacetime outside your light cone are not regions you could ever reach. c. Events outside your light cone cannot impact your future. d. All of the above. e. Only A and B.
E A and B are both correct statements. C is incorrect because events outside your light cone can affect your future. For example light emitted at an event outside your light cone could propagate into your light cone and send a signal that would impact your future.
How do astronomers see astrophysical black holes if no light can escape from the event horizon of the black hole? a. We look for light emitted by matter close to the black hole that has not yet crossed the event horizon. b. We look for the black hole's gravitational effect on the motion of nearby stars. c. We look for the emission from the black holes corresponding white hole. d. All of the above e. Both a and b
E Both a and b are true and were mentioned at the start of lecture 27. Black holes do emit hawking radiation, but the wavelengths are much too small and the radiation too faint for us to see such radiation.
If you are traveling at a large fraction of the speed of light (v = 0.99c) down a city street and facing forward in the direction in which you are moving, what would you see? a. Nothing abnormal, but everyone would seem to move really slowly. b. Buildings would be shorter along the direction of motion, but would otherwise look normal. c. The shapes of buildings would be distorted and colors would be unchanged. d. The shapes of buildings would be distorted and the colors would be redshifted. e. The shapes of buildings would be distorted and the colors would be blue-shifted.
E Due an effect called relativistic aberration, the appearance of objects is significantly distorted as speeds close to the speed of light. Furthermore, since objects appear to be coming toward you at large velocity, they are relativistically Doppler shifted towards short wavelengths (i.e. blueshifted).
If luminosity is proportional to mass to the 3.5 power (L∝M₃.₅)(L∝M₃.₅), how many times more luminous is a 100 solar mass star than the Sun? a. 100 times more luminous b. 350 times more luminous c. thousand times more luminous d. million times more luminous e. 10 million times more luminous
E E is correct because 100^3.5 = (10²)^3.5 = 10⁷ or 10 million times more luminous.
What sort of remnants do massive star supernova leave behind after they explode? a. Black holes b. Neutron stars c. White dwarves d. All of the above e. Only A and B
E Massive star supernovae lead to neutron stars and black holes. White dwarfs are produce by low mass stars after their planetary nebula phase
Which is an accurate description of the singularity in a Schwarzschild black hole? a. It is an infinitesimally small point in space at the black hole's center. b. It is a spacetime surface where the spacetime curvature is infinite. c. It is a spacetime surface where any matter crossing the event horizon must end up. d. All of the above e. Only B and C
E Only B and C are correct. The singularity is a spacetime surface where matter crossing the event horizon must end up and it is a surface of infinite spacetime curvature. It is not an infinitesimal point in space. This is a misconception because the radial coordinate switches to being time-like inside the horizon.
Why do some astrophysical objects form spheres and others form disks? a. Disks form when the initial distribution of matter is created by an explosion of a spherical object. b. Disks form when the initial distribution of matter has low angular momentum. c. Disks form when the initial distribution of matter is very cold. d. Disks form when the initial distribution of matter is very hot. e. Disks form when the initial distribution of matter has high angular momentum.
E The correct answer is E. The primary distinction between the formation of disks and spheres is how much angular momentum the object has. When most objects form gravity pulls in objects from large distances. As it contracts, if it has lots of angular momentum, it will tend to form a disk.
How do the effects of general relativity affect the emission from neutron stars? a. The emission is gravitationally redshifted b. We can receive light from more than half the star because of the bending of light by gravity. c. Some of the light cannot reach us because it is trapped by the neutron star's gravity d. All of the above. e. Only A and B
E The first two effects are both present so both A and B are true. These should be familiar from our discussion of black holes and general relativity. Even light from Earth's surface is redshifted, but the effect is much larger in neutron stars - almost as large as the redshift at the ISCO of a black hole. Similarly, the gravity of the star acts as a lens in much the same way the black hole's gravity does. However, unlike a black hole, there is no event horizon so any light radiated from the surface can escape to infinity so c is false.
What do physicists mean when they say that energy is conserved? a. Energy is not wasted. b. The energy of a closed system can go up or stay the same, but never decrease. c. The energy of a closed system can go down or stay the same, but never increase. d. The forms of energy in a closed system must remain the same. e. The forms of energy in a closed system can change, but the sum of all forms of energy must remain the same.
E This is discussed in lecture 4.
Based on Newton's law of universal gravitation, what is the acceleration due to gravity at the surface of the Earth in terms of Newton's constant G, the mass of the Earth Mₑ, and the radius of the Earth Rₑ? a. Mₑ/GRₑ b. GMₑ/Rₑ c. GM²ₑ/R²e d. GM²ₑ/Rₑ e. GMₑ/R²ₑ F. none of the above
E This problem requires using the F = ma and F = GM m/r² formulas and doing some algebra. Given any mass m on the surface of the Earth, we have that the gravitational force due to Earth is F=G Mₑ m / Rₑ². We can find the acceleration to this force via a = F/m. Inserting F from gravity into this yields a = G Mₑ m / (Rₑ² m). The m's in the numerator and denominator cancel, leaving a = G Mₑ / Rₑ², which corresponds to E.
An evil physicist decides she wants to blow up the Earth by detonating an antimatter bomb in the center of the planet. She estimates that this will take about 2 x 10³² Joules (the gravitational binding energy of the Earth). Since only half the of the bomb needs to be anti-matter (the other half can just be normal matter at the center of the Earth), how much anti-matter does she need to create for her bomb. (One metric ton = 1000 kg.) a. one metric ton b. one thousand metric tons c. one million metric tons d. one billion metric tons e. one trillion metric tons
E We know that E=mc² so we need to solve for m = E/c²=(2 x 10³² J)/(3 x 10⁸ m/s)2 = 2 x 10¹⁵ kg = 2 x 10¹² metric tons but we divide by 2 since only half needs to be antimatter. 10¹² corresponds to one trillion so E is correct. This is a very large amount of antimatter.
Match the metric with the type of black hole. - Schwarzschild - Reissner-Nordstrom - Kerr - Kerr-Newman
Schwarzschild - no charge, no spin Reissner-Nordstrom - charged, no spin Kerr - no charge, spinning Kerr-Newman - charged, spinning
Based on the cartoon image of a roller coaster, answer the following questions.
The point of maximum potential energy is: - (a) The point where kinetic energy is increasing is - (b) The point of maximum kinetic energy is: - (c) Gravitational potential energy is largest and the maximum distance from the Earth (a in the picture). At point (b) the kinetic energy is increasing as potential energy is converted to kinetic energy. At point (c) kinetic energy is at a maximum.
Among these five pairs of objects, rank them from weakest to strongest gravitational force. (Remember to set the < signs when doing the ranking.) asteroid - asteroid Sun - asteroid Earth - asteroid asteroid - astronaut Moon - asteroid
asteroid - astronaut < asteroid - asteroid < Moon - asteroid < Earth - asteroid < Sun - asteroid Since the problem does not say anything about distance, you are free to assume that they are all at the same location. Otherwise, there would be no way to answer the problem. Then, the force is simply equal to the product of the masses. Since one of the masses (asteroid) is the same for all choices, you simply need to order them by the mass of the second object, from smallest to largest.
