ESSENTIAL COSMIC PERS.-W/MASTER.ACCESS
9th Edition
ISBN: 9780135795750
Author: Bennett
Publisher: PEARSON
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Chapter 14, Problem 36EAP
Black Holes in Popular Culture. Expressions such as “it disappeared into a black hole” are now common in popular culture. Give a few other examples of popular expressions in which the term black hole is used but is not meant to be taken literally. In what ways are these uses correct in their analogies to real black holes? In what ways are they incorrect? Why do you think such an eso-teric scientific idea as that of a black hole has captured the public imagination?
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What is a black hole. Explain
What is the Schwarzschild radius (in km) of a 6Msun black hole?
What fraction of the Earth's radius is this?
What percent of the speed of light (2.998 x 108 m/s) is the escape velocity at the Schwarzschild radius?
Part 1 of 3
The Schwarzschild radius of a black hole is given by:
2GM
Rs
=
c2
so for the given mass,
2G(6)(Msun)
Rs
c2
where M.
Sun = 1.99 x 1030 kg.
Then convert this into kilometers using 1 km = 1,000 m.
Rs
km
Part 1. Stellar Mass Black Holes
These are the collapsed cores of massive stars which end their life in supernova explosions. The
stellar core can no longer use nuclear fusion to hold up the immense gravity, and collapses until
its escape velocity rises higher than the speed of light. Voila! A black hole is formed.
Part A: The Schwarzschild Radius
The Schwarzschild Radius is defined as:
2GM
(1)
=
c2
where r, is the Schwarzschild radius, G is the gravitational constant, M is the mass of the black
hole, and c is the speed of light.
1. Let's say we have a black hole with a mass 10 times that of the Sun (the Sun's mass is 2 x
1030 kg, so the mass of the black hole is then 2 x 1031 kg). Using the definitions for G and
c, what would the Schwarzschild radius of this black hole be?
2. If the radius of the Sun is 7 x 108 m, how does the black hole's radius compare? (Divide
the radius of the Sun by the Schwarzschild radius). Your answer should be in the form of
times smaller/bigger than the…
Chapter 14 Solutions
ESSENTIAL COSMIC PERS.-W/MASTER.ACCESS
Ch. 14 - Prob. 1VSCCh. 14 - Prob. 2VSCCh. 14 - Prob. 3VSCCh. 14 - Prob. 4VSCCh. 14 - Prob. 5VSCCh. 14 - Prob. 1EAPCh. 14 - Prob. 2EAPCh. 14 - Prob. 3EAPCh. 14 - Prob. 4EAPCh. 14 - Prob. 5EAP
Ch. 14 - Prob. 6EAPCh. 14 - Prob. 7EAPCh. 14 - Prob. 8EAPCh. 14 - Prob. 9EAPCh. 14 - Prob. 10EAPCh. 14 - Prob. 11EAPCh. 14 - Prob. 12EAPCh. 14 - Prob. 13EAPCh. 14 - Prob. 14EAPCh. 14 - Prob. 15EAPCh. 14 - Prob. 16EAPCh. 14 - Prob. 17EAPCh. 14 - Prob. 18EAPCh. 14 - Prob. 19EAPCh. 14 - Prob. 20EAPCh. 14 - Prob. 21EAPCh. 14 - Prob. 22EAPCh. 14 - Prob. 23EAPCh. 14 - Prob. 24EAPCh. 14 - Gravitational waves are best observed with the...Ch. 14 - Prob. 26EAPCh. 14 - Prob. 27EAPCh. 14 - Prob. 28EAPCh. 14 - Prob. 29EAPCh. 14 - Prob. 30EAPCh. 14 - Prob. 31EAPCh. 14 - Viewed from a distance, how would a flashing red...Ch. 14 - Which of these black holes exerts the weakest...Ch. 14 - Current evidence indicates that most gamma-ray...Ch. 14 - Prob. 35EAPCh. 14 - Black Holes in Popular Culture. Expressions such...Ch. 14 - Too Strange to Be True? Despite strong theoretical...Ch. 14 - 37. Unanswered Questions. You have seen in this...Ch. 14 - Prob. 41EAPCh. 14 - Prob. 42EAPCh. 14 - Prob. 43EAPCh. 14 - Prob. 44EAPCh. 14 - Prob. 45EAPCh. 14 - Prob. 46EAPCh. 14 - Prob. 47EAPCh. 14 - Prob. 48EAPCh. 14 - Surviving the Plunge. The tidal forces near a...Ch. 14 - Black Holes. Andrew Hamilton, a professor at the...Ch. 14 - Prob. 51EAPCh. 14 - Prob. 52EAPCh. 14 - Prob. 53EAPCh. 14 - Prob. 54EAPCh. 14 - Prob. 55EAP
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- what is the mass of the black hole ? give your answer as a multiple of Ms where Ms is the solar mass, Ms = 2.0 * 10^(30) express your answer as a multiple of the solar mass mass Ms.arrow_forwardWhich statement concerning black hole masses and Schwarzschild radii is not true? A. Even an object as small as you could become a black hole if there were some way to compress you to a size smaller than your Schwarzschild radius. B. The more massive the black hole, the larger the Schwarzschild radius. C. For black holes produced in massive star supernovae, Schwarzschild radii are typically a few to a few tens of kilometers. D. In a binary system with a black hole, the Schwarzschild radius depends on the distance from the black hole to the companion star.arrow_forwardSuppose you drop a clock toward a black hole. As you look at the clock from a high orbit, what will you notice? Time on the clock will run faster as it approaches the black hole, and light from the clock A. will be increasingly blueshifted. B. The clock will fall toward the black hole at a steady rate, so that you'll see it plunge through the event horizon within just a few minutes. C. The clock will fall faster and faster, reaching the speed of light as it crosses the event horizon. D. Time on the clock will run slower as it approaches the black hole, and light from the clock will be increasingly redshifted.arrow_forward
- GM What is the orbital period of a bit of matter in an accretion disk that is located 3 x 105 km from a 29 M. black hole? (Hint: Use the circular orbit velocity formula, V. = Varrow_forwardExplain what is meant by the Schwarzschild radius of a black hole. Using a Newtonian approx- imation, derive an expression for the Schwarzschild radius, R, of a black hole of mass MBH- Calculate the Schwarzschild radius for a body with mass equal to the Sun's mass, and express your answer in units of kilometres.arrow_forwardWhat is the minimum escape velocity from the "surface" of a black hole? Group of answer choices The speed of light. About 6 times the Earth's escape velocity. 12,000 km/s 31,425 km/sarrow_forward
- a. What is the event horizon radius [m] for the sun if it were to collapse to a Schwarzschild black hole? (Msun = 1.99 x 1030kg). b. Would earth’s orbit be altered if this were to occur (T/F).arrow_forwardEvent Horizon is a region around a black hole where: group of answer choices: even light cannot escape. all the events are occurring speed of an object is close to speed of light. no physical object can pass through. r nothing can enter .arrow_forwardWhat would be the Schwarzschild radius, in light years, if our Milky Way galaxy of 100 billion stars collapsed into a black hole? Compare this to our distance from the center, about 13,000 light years.arrow_forward
- A black hole is an object with mass, but no spatial extent. It truly is a particle. A black hole may form from a dead star. Such a black hole has a mass several times the mass of the Sun. Imagine a black hole whose mass is ten times the mass of the Sun. a. Would you expect the period of an object orbiting the black hole with a semimajor axis of 1 AU to have a period greater than, less than, or equal to 1 yr? Explain your reasoning. b. Use Equation 7.6 to calculate this period.arrow_forwardWhat characteristics must a binary star have to be a good candidate for a black hole? Why is each of these characteristics important?arrow_forwardAs an object falls into a black hole, tidal forces increase. Will these tidal forces always tear the object apart as it approaches the Schwarzschild radius? How does the mass of the black hole and size of the object affect your answer?arrow_forward
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