PHYS 1303, Chap. 22, Homework, Prof. Kaim, DMC

Why do astronomers think that gamma-ray bursts are very distant and very energetic?

-Gamma ray bursts have to pass through something, which heats it up and causes it to glow. -You can see it optically and use red-shift blue-shift to measure distance.

Describe two leading models for gamma ray bursts

-short GBR- 30 seconds/ neutron stars smacking into each other=black hole -long GBR- 2-3 minutes/ hyper nova imploding

The special theory of relativity.

1) the speed of light is the maximum speed in the universe and all observers measure the same value for the speed of light regardless of their motion. 2) There is no absolute frame of reference in the universe; there is no way to tell who is moving and who is not. Only relative velocities between observers matter. 3) Neither space nor time can be considered independently of one another. Rather, they are components of a single entity: space time.

If a star is massive enough, it will collapse into a stellar-sized black hole when it runs out of fuel for nuclear burning. Since light cannot escape from black holes, they must be indirectly observed. One of the ways astronomers search for black holes is to look for the gravitational effects of a black hole on a nearby star. The figure below shows a binary system containing a blue super-giant and a stellar-mass black hole. Label the components of this binary system. a) Super-giant companion b) Black Hole c) Accretion disk d) Mass transfer stream

1. Super-giant Companion 2. Mass transfer stream 3. Black Hole 4. Accretion Disk (The figure shows how a black hole in a binary system can be detected. The strong gravitational force of the black hole pulls matter from a nearby companion star into a disk of gas known as an accretion disk. As gas transfers from the companion star to the black hole and accretes onto the black hole, the gas is heated to temperatures up to several million kelvins. The high temperature gas in the accretion disk emits X rays that astronomers can observe and use to determine the mass of the unseen companion. If the mass is greater than three solar masses, the object is likely a black hole.)

What are pulsars, and how are they related to neutron stars? Why aren't all neutron stars seen as pulsars?

According to the lighthouse model, neutron stars, because they are magnetized and rotating, send regular bursts of electromagnetic energy into space. The beams are produced by charged particles confined by the strong magnetic fields. When we can see the beams from Earth, we call the source a pulsar.

What evidence is there for black holes much more massive than the Sun?

Astronomers have found that stars and gas near the centers of many galaxies are moving extremely rapidly, orbiting some very massive unseen object. Masses inferred from Newton's laws range from millions to billions of times the mass of the sun. The intense energy emission from the centers of these galaxies and the short timescale fluctuations in that emission suggest the presence of massive, compact objects.

According to special relativity, what is special about the speed of light?

Can't change it and nothing is faster.

The formation of a black hole Stellar-sized black holes form when a star explodes in a supernova, leaving behind enough material that collapses to a distance within the black hole's Schwarzschild radius. As the core of the star collapses, its gravity becomes so strong that nothing—not even light—can escape from it. Sort the following stars according to whether they could or could not collapse into black holes. a) The Sun (1 solar masses) b) Spica A (11 solar masses) c) Sirius A (2 solar masses) d) Eta Carinae (100 solar masses) e) Betelgeuse (18 solar masses) f) Xi Persei (40 solar masses)

Could Collapse Into A Black Hole d) Eta Carinae (100 solar masses) f) Xi Persei (40 solar masses) Could NOT Collapse Into A Black Hole e) Betelgeuse (18 solar masses) b) Spica A (11 solar masses) c) Sirius A (2 solar masses) a) The Sun (1 solar masses) (Massive stars with a main-sequence mass greater than about 25 solar masses meet the lower mass limit required for the stars' cores to collapse into black holes following a supernova. The cores of less massive stars, or stars with less than about 25 solar masses, will become either white dwarfs or compact objects known as neutron stars after the star runs out of nuclear fuel for fusion.)

Listed following are several astronomical objects. Rank these objects based on their density, from highest to lowest. a) one solar mass white dwarf b) singularity of a black hole c) typical neutron star d) main sequence star

Highest Density b) singularity of a black hole c) typical neutron star a) one solar mass white dwarf d) main sequence star Lowest Density (The singularity of a black hole is a place where density approaches infinity, so it is clearly the most dense of the objects shown. Neutron stars are much more dense than white dwarfs, which in turn are much more dense than main-sequence stars.)

Why is it so difficult to test the predictions of general relativity? Describe two tests of the theory.

It is difficult to test because it's effects on earth and in the solar system - the places where we can most easily perform tests - are very small. 1- the deflection of light by the sun 2- the effect of relativity on the orbit of mercury

Imagine that you are located on Earth while a spaceship travels from Earth to the star Vega at constant velocity of 0.8c. The following items describe quantities that, according to Einstein's special theory of relativity, would be either larger (or longer), smaller (or shorter), or the same as their rest values. (Note that by "rest value," we mean the value you would find if both you and the spaceship were at rest on Earth.) Match each item to the correct category. a) one second on a spaceship clock as seen by you b) distance to Vega as measured by spaceship passengers c) mass of spaceship as measured by you d) your mass as measured by spaceship passengers e) one second on your clock as seen by spaceship passengers f) speed of the spaceship's headlight as measured by you g) length (in the direction of motion) of the spaceship as measured by you

Larger/Longer than Rest Value e)one second on your clock as seen by spaceship passengers a) one second on a spaceship clock as seen by you c) mass of spaceship as measured by you d) your mass as measured by spaceship passengers Smaller/Shorter than Rest Value b) distance to Vega as measured by spaceship passengers g) length (in the direction of motion) of the spaceship as measured by you Same as Rest Value f) speed of the spaceship's headlight as measured by you (You consider yourself to be at rest and say that the spaceship is traveling at constant velocity of 0.8c. Therefore, your measurements of the spaceship will show length contraction, making it shorter; time dilation, which means you see time on the spaceship running slower than time for you, so that one second on the spaceship clock is longer than one second for you; and mass increase for the spaceship, making its mass larger than its rest mass. But passengers on the spaceship would say that they are at rest while you and Earth and Vega are traveling relative to them at constant velocity of 0.8c. Therefore their measurements will show length contraction for you, Earth and Vega, making the Earth-Vega distance shorter; time dilation for you, which means they see your time running slower then theirs, so that one second on your clock lasts longer than one second for them; and mass increase for you, making your mass larger than your rest mass.)

Listed following are several astronomical objects. Rank these objects based on their diameter, from largest to smallest. (Note that the neutron star and black hole in this example have the same mass to make your comparison easier, but we generally expect black holes to have greater masses than neutron stars.) a) a two-solar-mass neutron star b) one-solar-mass white dwarf c) the event horizon of a two-solar-mass black hole d) Jupiter e) the moon f) main-sequence star of spectral type A

Largest Diameter f) main-sequence star of spectral type A d) Jupiter b) one-solar-mass white dwarf e) the moon a) a two-solar-mass neutron star c) the event horizon of a two-solar-mass black hole Smallest Diameter (The main-sequence star is obviously much larger than a planet such as Jupiter. A one-solar-mass white dwarf is about the size of Earth, which makes it larger than the Moon. A neutron star will be larger than a black hole of the same mass, because while light can escape from a neutron star, the same mass in a black hole must be more concentrated so that its gravity is strong enough to prevent light from escaping.)

Listed following are several astronomical objects. Rank these objects based on their mass, from largest to smallest. a) main-sequence star of spectral type M b) Jupiter c) typical neutron star d) a one solar mass white dwarf e) typical black hole (formed in a supernova) f) the moon

Largest Mass e) typical black hole (formed in a supernova) c) typical neutron star d) a one solar mass white dwarf a) main-sequence star of spectral type M b) Jupiter f) the Moon Smallest Mass (Note that while the rankings shown are correct for "typical" white dwarfs, neutron stars, and black holes, each of these objects comes in a range of masses and so there may be some exceptions.)

The figures below show several different astronomical objects. Rank the objects based on the amount that space-time is curved (relative to flat space-time) at a distance of 10 AU from the center of each of the objects, from least to greatest. If two (or more) cases are equal, show this equality by dragging one figure on top of the other(s). a) the Sun b) Red Giant mass=1 M_Sun, radius about 100 R_Sun c) Black Hole mass=1 M_Sun, radius (event horizon) about 3 km d) White Dwarf mass=1 M_Sun, radius about 0.01 R_Sun

Least Amount a-d are all the same - stack them on top of one another. Greatest Amount (Einstein's general theory of relativity tells us that gravity is curvature of space-time. From Part A, you already know that the strength of gravity at a distance of 10 AU is the same for all four cases (because all four objects have the same mass). Therefore the curvature of space-time is also the same in all four cases.)

The figures below show several different astronomical objects. Rank the objects based on the amount that space-time is curved (relative to flat space-time) very near the surface (or event horizon) of the objects, from least to greatest. a) Black hole, mass=1 M_Sun, radius (event horizon)=3 km b) Red giant, mass=1 M_Sun, radius=100 R_Sun c) White dwarf, mass=1 M_Sun, radius=0.01 R_Sun d) the Sun

Least Amount b) Red giant, mass=1 M_Sun, radius=100 R_Sun d) the Sun c) White dwarf, mass=1 M_Sun, radius=0.01 R_Sun a) Black hole, mass=1 M_Sun, radius (event horizon)=3 km Greatest Amount (It's important to understand how the combination of an object's mass and size both contribute to how much it will curve space-time.)

What is the principle of cosmic censorship? Do you think it is a sound scientific principle?

Nature always hides any singularity (place where the rules break down) such as that found at the center of a black hole, inside an event horizon. Even though physics fails, it's breakdown cannot affect us outside so we are safely insulated from any effects the singularity might have.

How does the way in which a neutron star forms determine some of its most basic properties?

Neutronization- iron core collapsed, protons & electrons are combined into a neutron ball

What is an event horizon? What would happen to someone falling into a black hole as they approach the event horizon?

Part 1: a theoretical boundary around a black hole beyond which no light or other radiation can escape. Part 2: Falling into a black hole would be subject to gravitational red-shift as the light climbed out of the hole's intense gravitational field. At the same time, a clock on the spaceship would show time dilation.

Although we cannot directly observe black holes, we can use theoretical models and Einstein's general theory of relativity to hypothesize about the structure of black holes. Label the main parts of a black hole on the figure below. a) singularity b) event horizon c) Schwarzchild radius

Radius Line: c) Schwarzchild radius Inside the Circle: a) Singularity Outline of Circle: b) Event horizon (Theoretical models show that a non-rotating black hole has a simple structure consisting of two main parts - a singularity and a boundary. All of the mass from the core of the massive star that became the black hole, as well as any additional accreted mass, will accumulate within the boundary of the black hole. The spherical boundary between the singularity and the rest of the universe is known as the event horizon, where the radius of the event horizon is the Schwarzschild radius.)

Part A: Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Assume that all the spaceships have equal length when at rest and that you watch the other spaceship as its clock ticks off one second. Rank the figures based on the length that you would measure for the other spaceship (in its direction of motion), from shortest to longest. a) Speed= 0.85c b) Speed= 0.7c c) Speed= 0.8c d) Speed= 0.75c

Shortest Length a) Speed= 0.85c c) Speed= 0.8c d) Speed= 0.75c b) Speed= 0.7c Longest Length (The faster an object is moving relative to you, the shorter (in its direction of motion) you will measure it to be.)

Part B: Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Assume that all the spaceships have equal length when at rest and that you watch the other spaceship as its clock ticks off one second. The four figures below are the same as those in Part A. This time, rank the figures based on your length as measured by the passenger in the other spaceship, from shortest to longest. a) Speed= 0.8c b) Speed= 0.75c c) Speed= 0.85c d) Speed= 0.7c

Shortest Length c) Speed= 0.85c a) Speed= 0.8c b) Speed= 0.75c d) Speed= 0.7c Longest Length (The passenger on the other ship must observe the same effects on you as you observe on her, because both of you are in free-float reference frames and there is no way to say who is "really" moving. In other words, just as you say that her ship is contracted in length, she says that your ship is contracted in length. That is why the answer here is the same as the answer in Part A.)

Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Imagine that you watch the other spaceship as its clock ticks off one second. Rank the figures according to how much time you would say passes (on your own ship) while the other ship's clock ticks off one second, from the shortest to the longest amount of time. a) Speed= 0.7c b) Speed= 0.85c c) Speed= 0.8c d) Speed= 0.75c

Shortest Time a) speed = 0.7c d) speed = 0.75c c) speed = 0.8c b) speed = 0.85c Longest Time (The faster an object is moving relative to you, the slower its time will run relative to yours. Slower time means its clock takes longer to tick off each second, which is why the rankings go in order of increasing speed (relative to YOU).)

The four figures below are the same as those in Part A. This time, imagine that the passengers on the other spaceship are watching your clock as its ticks off one second. Rank the figures according to how much time the passengers (on the other ship) would say passes (on their ship) while they watch your clock tick off one second, from the shortest to the longest amount of time. a) speed = 0.8c b) speed = 0.85c c) speed = 0.7c d) speed = 0.75c

Shortest Time c) speed = 0.7c d) speed = 0.75c a) speed = 0.8c b) speed = 0.85c Longest Time (The passengers on the other ship must observe the same effects on you as you observe on them, because both of you are in free-float reference frames and there is no way to say who is "really" moving. In other words, just as you say time is running slow on their ship, they say time is running slow on your ship. That is why the answer here is the same as the answer in Part A.)

The figures below show several different astronomical objects. Rank the objects based on the acceleration a spaceship would have as it passed very near the surface (or event horizon) of each object, from smallest to largest. a) Black hole, mass=1 M_Sun, radius (event horizon)=3 km b) the Sun c) Red giant, mass=1 M_Sun, radius=100 R_Sun d) White dwarf, mass=1 M_Sun, radius=0.01 R_Sun

Smallest Acceleration b) Red giant, mass=1 M_Sun, radius=100 R_Sun d) the Sun c) White dwarf, mass=1 M_Sun, radius=0.01 R_Sun a) Black hole, mass=1 M_Sun, radius (event horizon)=3 km Largest Acceleration (From Part C you know that spacetime is curved more — which is equivalent to saying that gravity is stronger — near the surface (or event horizon) of the objects with smaller radii. Stronger gravity causes greater acceleration to an object passing nearby, which is why the ranking here is the same as that from Part C.)

Do you think that planet-size objects orbiting a pulsar should be called planets? Why or why not?

The planetary system orbiting the pulsar's parent star was almost certainly destroyed in the supernova explosion that created the pulsar. As a result, the scientists are still uncertain about how these planets came into being. One possibility involves the binary companion that provided the matter necessary to spin the pulsar up to millisecond speeds. Hence, the planet-size objects discovered orbiting a pulsar can be called a planet.

Use your knowledge of escape speed to explain why black holes are said to be "black."

Their escape speed is higher than the speed of light- everything is moving towards it.

What are X-ray bursters?

They are neutron stars on which accreted matter builds up, then explodes in a violent nuclear explosion.

What is the favored explanation for the rapid spin rates of millisecond pulsars?

They consume a lot of matter, very fast, and they rotate really quickly.

Neutron stars have four basic properties:

a small diameter high density strong gravity strong magnetic field (additionally: sometimes appears as a pulsar, fast rotation, radio emission

The figures below show several different astronomical objects. Rank the objects based on the strength of the gravitational force that would be felt by a spacecraft traveling at a distance of 10 AU from the center of each of the objects, from weakest to strongest. If the gravitational force is equal for two (or more) cases, show this equality by dragging one figure on top of the other(s). a) the Sun b) Red Giant mass=1 M, radius about 100R_Sun c) Black Hole mass=1 M, radius (event horizon) about 3 km d) White Dwarf mass=1M_Sun, radius about 0.01R_Sun

Weakest Force a-d are all the same - stack them on top of one another. Strongest Force (A distance of 10AU is far from all four objects (the red giant's radius of 100 RSun is equivalent to only about 1 AU), so the gravitational force on the spacecraft depends only on this distance, the spacecraft's mass, and the mass of the object the spacecraft is orbiting. Since all four objects have the same mass, the gravitational force is the same in all four cases.)

Listed following are distinguishing characteristics of different end states of stars. Match these to the appropriate consequence of stellar death. a) sometimes appears as a pulsar b) viewed from afar, time stops at its event horizon c) has a mass no greater than 1.4M Sun d) in a binary system, it can explode as a supernova e) usually has a very strong magnetic field f) typically about the size (diameter) of Earth g) supported by electron degeneracy pressure h) size defined by its Schwarzschild radius

White Dwarf: d) in a binary system, it can explode as a supernova c) has a mass no greater than 1.4M Sun f) typically about the size (diameter) of Earth g) supported by electron degeneracy pressure Neutron Star: e) usually has a very strong magnetic field a) sometimes appears as a pulsar Black Hole: h) size defined by its Schwarzschild radius b) viewed from afar, time stops at its event horizon

Conditions inside of and near a black hole can be described using Einstein's general theory of relativity. The theory's basic premise is that matter curves space-time, and this curvature tells matter how to accelerate. Based on general relativity, how do black holes affect space-time, matter, and radiation in their region? a) Around a black hole and within the event horizon, space-time is curved to the extent that space folds over on itself. b) As matter and radiation approach a black hole, they continue on their original path with no change in motion. c) Space-time is minimally curved around a black hole, causing matter and radiation to remain visible and only slightly change their direction of motion. d) As matter and radiation approach a black hole, they react to the curvature of space-time by significantly changing their direction of motion. e) Matter and radiation that fall inside a black hole's event horizon can no longer be detected by an outside observer. f) Matter and radiation that fall inside a black hole's event horizon can be detected by an outside observer.

a) Around a black hole and within the event horizon, space-time is curved to the extent that space folds over on itself. d) As matter and radiation approach a black hole, they react to the curvature of space-time by significantly changing their direction of motion. e) Matter and radiation that fall inside a black hole's event horizon can no longer be detected by an outside observer. (According to Einstein's theory of general relativity, if you were approaching a black hole you would be greatly accelerated by the extremely curved space-time surrounding a black hole. It also means that the large curvature in space-time surrounding a black hole and the associated large escape speed cuts off all communication between the black hole and anything outside of the event horizon. Therefore, once matter crosses the event horizon, any telescopic instrument outside of the black hole cannot detect it.)

If the Sun were magically to turn into a black hole of the same mass, a) Earth's orbit would remain unchanged. b) Earth would fly off into space. c) Earth would start to spiral inward. d) Earth would be torn apart.

a) Earth's orbit would remain unchanged.

In addition to having indirect observational evidence for stellar-sized black holes in binary systems, astronomers also have indirect observational evidence of super-massive black holes at the centers of galaxies. If you were tasked with finding a super-massive black hole, which of the following observations could you present as evidence that a super-massive black hole exists in a galaxy? Choose all that apply. a) High-energy jets of gas are observed coming from the galactic center. b) Stars and gas near the center of the galaxy exhibit rapid orbital velocities in a fairly small region of space. c) Stars and gas near the center of the galaxy disappear when they pass behind the center of the galaxy, causing a periodic decrease in the galaxy's brightness. d) The center of the galaxy emits pulses of radio waves over very short time periods.

a) High-energy jets of gas are observed coming from the galactic center. b) Stars and gas near the center of the galaxy exhibit rapid orbital velocities in a fairly small region of space. (Evidence for super-massive black holes comes from observations of many galactic centers. Astronomers have observed stars and gas moving about galactic centers at high speeds that indicate the presence of a very massive object - on the order of millions to billions of solar masses. Since no objects have been directly detected at the centers of galaxies, astronomers believe that the stars and gas are orbiting around unseen super-massive black holes. Other evidence for super-massive black holes at the centers of galaxies comes from observing high-energy jets in active galaxies. It is not entirely known how these jets form, but they appear to be associated with the accretion disk and magnetic field surrounding a super-massive black hole.)

The properties of neutron stars help explain their relationship to pulsars. Which of the following is (are) important when explaining how a pulsar generates the radiation we detect? Choose all that apply. a) Neutron stars can rotate extremely rapidly, as quickly as 30 times a second or more. b) A neutron star is a dense sphere composed almost entirely of compressed neutrons with a mass one to three times that of the Sun. c) The magnetic field lines in a neutron star are squeezed close together, creating an extremely intense magnetic field. d) The extremely high temperatures produce gamma rays from fusion in the neutron star.

a) Neutron stars can rotate extremely rapidly, as quickly as 30 times a second or more. c) The magnetic field lines in a neutron star are squeezed close together, creating an extremely intense magnetic field.

Consider again the spaceships from Parts A and B. Suppose that, at rest, both you and a passenger on the other spaceship have the same heart rate of 60 beats per minute. How will you and the passenger on the other spaceship observe each other's heart rates as you pass by in your spaceships? a) You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers. b) You would observe that the passenger in the other spaceship has a faster heart rate than you do, and she would observe that you have a slower heart rate than hers. c) You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a faster heart rate than hers. d) Both of you would observe that your hearts are beating in sync at the same rate.

a) You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers. (Strange as it may sound, you will claim that time is running slow on her spaceship while she will claim that time is running slow on your spaceship. This is an example of what Einstein told us when he discovered that measurements of time and space are relative.)

If there is a black hole in a binary system with a blue super-giant star, the X-ray radiation we may observe would be due to the a) accretion disk of material falling into the black hole b) radiation from inside the event horizon of the black hole c) super-giant star

a) accretion disk of material falling into the black hole (Looking for these small, point-like X-ray sources in binary systems is an important first step in finding black hole candidates.)

Gamma-ray bursts are observed to occur a) approximately uniformly over the entire sky. b) throughout the Milky Way Galaxy. c) mainly near the Sun. d) near pulsars.

a) approximately uniformly over the entire sky.

Why do black holes emit neither radiation nor other information? The answer to this question is related to the concept of escape speed—the speed necessary for one object to escape the gravitational pull of another object. The escape speed from an object depends entirely on its mass and radius. Consider a star of a given mass. If the star remains the same mass, but decreases in radius, its escape speed will _____. a) increase b) remain the same c) decrease

a) increase. (As a body's size decreases while its mass remains the same, it will become increasingly difficult for an object to escape the gravitational pull of that body. In other words, the body's size may become so small that the required escape speed is the speed of light. Black holes have reached such a limit, which is why it is impossible for radiation or other information to escape a black hole.)

As the falling rocket plunges toward the event horizon, an observer in the orbiting rocket would see that the falling rocket __________. a) slows down as it approaches the event horizon and never actually crosses the event horizon b) slows down near the event horizon so that it crosses the event horizon at a low speed c) moves at constant speed as it approaches and crosses the event horizon d) accelerates as it falls and crosses the event horizon at high speed

a) slows down as it approaches the event horizon and never actually crosses the event horizon (Viewed from afar, time comes to a stop at the event horizon of a black hole, so falling objects never appear to cross the event horizon.)

The most rapidly "blinking" pulsars are those that a) spin fastest; b) are oldest; c) are most massive; d) are hottest.

a) spin fastest;

Figure 1 shows the stick's measured length aboard the moving ship. Part A According to the figure, a meter stick in a spaceship traveling at half the speed of light would appear to have a length of a) 1 meter b) 0.87 meter c) 0.50 meter d) 0.15 meter

b) 0.87 meter

According to the Figure in Discovery 22-1, a meter-stick in a spaceship traveling at half of the speed of light would appear to have a length of a) 1 meter; b) 0.87 meter; c) 0.50 meter; d) 0.15 meter.

b) 0.87 meter;

Detecting a black hole is a challenging endeavor for astronomers. Why is it so difficult for astronomers to observationally detect black holes? View Available Hint(s) Detecting a black hole is a challenging endeavor for astronomers. Why is it so difficult for astronomers to observationally detect black holes? a) Black holes reside in a region of space that is dark, empty, and undetectable by any astronomical instruments. b) Black holes have an escape speed that is greater than the speed of light. c) Black holes reside at the centers of bright stars, whose light outshines the light emitted from the black holes. d) Black holes emit radiation only once every few thousand years.

b) Black holes have an escape speed that is greater than the speed of light. (All of a black hole's mass is contained within the relatively small region of space defined by its Schwarzschild radius. This small radius causes the black hole to have an escape speed that is greater than the speed of light. Radiation from within a black hole has no way of escaping into space, so the black hole emits no detectable radiation. This makes it very difficult for astronomers to observationally detect black holes.)

The best evidence for super-massive black holes in the centers of galaxies is a) the absence of stars there; b) rapid gas motion and intense energy emission; c) gravitational red-shift of radiation emitted from near the center; d) unknown visible and X-ray spectral lines.

b) rapid gas motion and intense energy emission;

We can summarize the results of Parts A and B as follows: When another spaceship is moving by you (at constant velocity), you will measure the spaceship to be shorter than its rest length, while passengers on that ship will measure your length to be shorter. Imagine that you and the passengers on the other ship are arguing (by radio) about who really is the one that has become shorter. To settle the argument, you agree to meet up on Mars and put the two spaceships next to each other to see which one is really shorter. What will you find when you meet up on Mars? a) Your spaceship really is shorter than the other one. b) Both spaceships are the same length. c) The other spaceship really is shorter than yours.

b) Both spaceships are the same length. (Once you put the two spaceships next to one another, you are in the same reference frame and therefore everyone will agree that the two ships have the same length. The lengths differ only when the ships are moving relative to each other, and of course you cannot compare the ships next to one another while they are moving.)

If the Sun were to magically turn into a black hole of the same mass, a) Earth would start to spiral inward; b) Earth's orbit would remain unchanged; c) Earth would fly off into space; d) Earth would be torn apart.

b) Earth's orbit would remain unchanged;

From Part B, you know that from afar you'll never see the in-falling rocket cross the event horizon, yet it will still eventually disappear from view. Why? a) Even though you won't see it cross the event horizon, it does cross it, and that means you can no longer see it. b) Its light will become so red-shifted that it will be undetectable. c) The black hole's blackness will drown out the light of the rocket. d) Tidal forces will squeeze the in-falling rocket to an undetectably thin line.

b) Its light will become so red-shifted that it will be undetectable. (As the video shows, viewed from afar the light of the in-falling rocket becomes increasingly red-shifted. As it approaches the event horizon, the redshift approaches infinity, meaning all its light is stretched to such enormous wavelengths that no detector could see it, even in principle.)

From the viewpoint of an observer in the orbiting rocket, what happens to time on the other rocket as it falls toward the event horizon of the black hole? a) Time runs increasingly faster as the rocket approaches the black hole. b) Time runs increasingly slower as the rocket approaches the black hole. c) Time is always the same on both rockets.

b) Time runs increasingly slower as the rocket approaches the black hole. (In this video, your view is similar to the view from the orbiting rocket. Notice that the clock on the falling rocket ticks more slowly as it approaches the black hole, indicating that time is slowing down.)

A neutron star is about the same size as a) a school bus; b) a U.S. city; c) the Moon; d) Earth.

b) a U.S. city;

If you were inside the rocket that falls toward the event horizon, you would notice your own clock to be running __________. a) increasingly faster as you approach the event horizon b) at a constant, normal rate as you approach the event horizon c) increasingly slower as you approach the event horizon

b) at a constant, normal rate as you approach the event horizon (All motion is relative, and you will always consider your own clock to be running at a normal rate.)

Black holes result from stars having initial masses a) less than the mass of the Sun; b) between one and two times the mass of the Sun; c) up to eight times the mass of the Sun; d) more than 25 times the mass of the Sun.

b) between one and two times the mass of the Sun;

The X-ray emission from a neutron star in a binary system comes mainly from a) the hot surface of the neutron star itself. b) heated material in an accretion disk around the neutron star. c) the surface of the companion star. d) the neutron star's magnetic field.

b) heated material in an accretion disk around the neutron star.

A neutron star's immense gravitational attraction is due primarily to its small radius and a) strong magnetic field. b) large mass. c) rapid rotation rate. d) high temperature.

b) large mass.

According to Jackie, __________. a) the green light illuminates her before the red light because she is traveling toward the green light b) the green light illuminates her before the red light because she sees the green light flash first c) the green light illuminates her at the same time as the red light because both flashes occur at the same time and at an equal distance from her. d) the green light illuminates her at the same time as the red light because she sees the green light flash after the red light

b) the green light illuminates her before the red light because she sees the green light flash first (As the diagram on the right shows clearly, the green light does indeed illuminate Jackie before the red light reaches her. Because Jackie perceives herself as stationary and both lights are located an equal distance away from her in her own spaceship, she can explain this fact only by saying that the green light source flashed first.)

Most binary systems with an invisible companion contain a large, bright star and a small, dim star hidden by the light of its larger companion. However, in some binary systems, the unseen companion may be a black hole instead of a small star. One of the most likely black hole candidates in a binary system is an object called Cygnus X-1. If you were an astronomer trying to prove that Cygnus X-1 is a black hole, which of the following observations would provide evidence in support of your claim? Choose all that apply. a) Cygnus X-1 has a mass one-tenth that of the Sun. b) Cygnus X-1 has a diameter much greater than 300 kilometers. c) Cygnus X-1 produces a large amount of X-ray emissions. d) Cygnus X-1 has a mass of 10 solar masses. e) Cygnus X-1 produces no X-ray emissions. f) Cygnus X-1 has a diameter less than 300 kilometers.

c) Cygnus X-1 produces a large amount of X-ray emissions. d) Cygnus X-1 has a mass of 10 solar masses. f) Cygnus X-1 has a diameter less than 300 kilometers. (An object that has a small diameter, emits lots of X rays, and has a mass greater than three solar masses is an excellent black hole candidate. Cygnus X-1 possesses all of these unique properties, which provides strong evidence that it is a black hole.)

Which of these statements do both you and Jackie agree are true? Consider the following five statements: 1. The green light and red light both flash at the same time. 2. The green light reaches Jackie before the red light reaches her. 3. The green light and red light reach you at the same time. 4. Jackie is the one who is moving. 5. The green light and red light travel at the same speed. Which of these statements do both you and Jackie agree are true? a) All five statements are true. b) Statements 1, 2, and 3 are true. c) Statements 2, 3, and 5 are true. d) Statements 1, 3, and 4 are true. e) Statements 2, 4, and 5 are true.

c) Statements 2, 3, and 5 are true. (You both agree on statements 2 and 3 because each of those describes a single event (that occurs in one place at one time), and all observers must agree on the reality of single events. You agree on Statement 5 because everyone always measures the same speed of light (and all wavelengths/colors of light travel at this same speed).)

If you were inside the rocket that falls toward the event horizon, from your own viewpoint you would __________. a) slow down and come to a stop at the event horizon b) slow down and cross the event horizon at low speed c) accelerate as you fall and cross the event horizon completely unhindered

c) accelerate as you fall and cross the event horizon completely unhindered (From your point of view, time runs normally in your spaceship and gravity must accelerate you as you fall toward the black hole. There is no physical barrier at the event horizon, so you cross it unhindered.)

The best place to search for black holes is in a region of space that a) is dark and empty; b) has recently lost some stars; c) has strong X-ray emission; d) is cooler than its surroundings.

c) has strong X-ray emission;

A neutron star's immense gravitational attraction is due primarily to its small radius and a) rapid rotation rate; b) strong magnetic field; c) large mass; d) high temperature.

c) large mass;

Part B Black holes... a) are the end states of stars like our Sun b) suck up everything in their vicinity, so orbits around them are not possible c) prevent anything inside the event horizon from escaping

c) prevent anything inside the event horizon from escaping (This is why we don't observe any radiation directly from the black hole, only from material being compressed and heated in the black hole's vicinity.)

The best evidence for super-massive black holes in the centers of galaxies is a) unknown visible and X-ray spectral lines. b) the absence of stars there. c) rapid gas motion and intense energy emission. d) gravitational redshift of radiation emitted from near the center.

c) rapid gas motion and intense energy emission.

The most rapidly "blinking" pulsars are those that a) are most massive. b) are hottest. c) spin fastest. d) are oldest.

c) spin fastest.

Neutron stars and pulsars are associated with a) the birth of massive stars b) the birth of low-mass stars c) the collapse and supernova explosion of massive stars d) the end stage of low-mass star evolution

c) the collapse and supernova explosion of massive stars (Many supernova remnants from massive star explosions are seen to contain evidence of neutron stars or pulsars.)

The X-ray emission from a neutron star in a binary system comes mainly from a) the hot surface of the neutron star itself; b) heated material in an accretion disk around the neutron star; c) the neutron star's magnetic field; d) the surface of the companion star.

c) the neutron star's magnetic field;

What does Jackie say about the lights as they illuminate you? a) The green light illuminates you before the red light because the green light flashed first. b) The red light illuminates you before the green light because you are traveling toward the red light. c) The green light illuminates you at the same time as the red light because both flashes occur at the same time. d) The green light illuminates you at the same time as the red light because although the green light flashes first, you are traveling away from it.

d) The green light illuminates you at the same time as the red light because although the green light flashes first, you are traveling away from it. (As the diagram on the left shows clearly, both lights reach you at the same time. Because this is a single, observable event, all observers must agree on its reality. The diagram on the right shows how Jackie explains this reality: From Part A, we know that Jackie claims that the green light flashed first. However, as shown in the right diagram, she sees you moving away from the green light and toward the red light, which means the green light must travel a greater distance to reach you than the red light. Therefore, even though the green light flashed first, the longer distance it must travel means it ends up reaching you at the same time as the red light.)

According to Figure 22.11, gamma-ray bursts are observed to occur a) mainly near the Sun; b) throughout the Milky Way Galaxy; c) approximately uniformly over the entire sky; d) near pulsars.

d) near pulsars.

What makes Cygnus X-1 a good black-hole candidate?

it is easily observed through its interaction with its partner star that is slowly being pulled towards it. X-ray images reveal the accretion disk around where either a black hole or a neutron star is, but the center of the accretion disk has to high of a mass limit to be a neutron star.

What would happen to a person standing on the surface of a neutron star?

they would be pulverized due to the high gravity, creating a new layer of crust; combined with a high rate of speed would create a huge explosion