Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 42Q
To determine
To explain:
The reason LIGO can’t detect gravitational waves
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What is the orbital period of a bit of matter in an accretion disk that is located 4 ✕ 105 km from a 87 M black hole? Use the circular orbit velocity formula.
As a mass m of gas falls into a black hole, at most 0.1mc2 is likely to emerge as radiation; the rest is swallowed by the black hole. Show the Eddington luminosity for a black hole of mass M is equivalent to 2*10-9 Mc2yr-1. Explain why we expect the black hole's mass to grow by at least a factor of e every 5*107 years. Where Edding Luminicity is defined as LE=(4piGMmpc)/(sigmaT), where G is the gravitational constant, M is the mass of the black hole, mp is the mass of a proton, c is the speed of light, and sigmaT is Thomson scattering where sigmaT=6.653*10-25 cm2.
I understand that to an outside observer, the light from a star
that is collapsing into a black hole will become more and more
red-shifted as the surface of the star appears to approach the
black hole event horizon. The outside observer will never actually
see the surface of the star cross the black hole event horizon.
This applies to all outside observers: at infinity, in orbit around
the star/black hole or those using a rocket to hover above the
black hole.
Conversely, I know that for someone on the surface of the star
that is collapsing to form a black hole it will appear quite
different. The observer on the surface will not see anything
unusual happen as they cross the event horizon and in a finite time
they will reach the singularity at the center of the black hole
where we do not know what will happen since general relativity
breaks down in a singularity.
So, now consider an observer that starts at a great distance
from the star who is continually falling directly into the star…
Chapter 21 Solutions
Universe: Stars And Galaxies
Ch. 21 - Prob. 1QCh. 21 - Prob. 2QCh. 21 - Prob. 3QCh. 21 - Prob. 4QCh. 21 - Prob. 5QCh. 21 - Prob. 6QCh. 21 - Prob. 7QCh. 21 - Prob. 8QCh. 21 - Prob. 9QCh. 21 - Prob. 10Q
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- The next step in deciding whether the object in Exercise 25.25 is a black hole is to estimate the density of this mass. Assume that all of the mass is spread uniformly throughout a sphere with a radius of 20 lighthours. What is the density in kg/km3? (Remember that the volume of a sphere is given by V=43R3 .) Explain why the density might be even higher than the value you have calculated. How does this density compare with that of the Sun or other objects we have talked about in this book?arrow_forwardA stellar black hole may form when a massive star dies. The mass of the star collapses down to a single point. Imagine an astronaut orbiting a black hole having eight times the mass of the Sun. Assume the orbit is circular. a. Find the speed of the astronaut if his orbital radius is r = 1 AU. b. Find his speed if his orbital radius is r = 11.8 km. c. CHECK and THINK: Compare your answers to the speed of light in a vacuum. What would the astronauts orbital speed be if his orbital radius were smaller than 11.8 km?arrow_forwardIf the Sun were to collapse into a black hole, the point of no return for an investigator would be approximately 3 km from the center singularity. Would the investingator be able to survive visiting even 300 km from the center? Answer this by finding the difference in the gravitatoinal attraction the black holes exerts on a 1.0-kg mass at the head and at the feet of the investigator.arrow_forward
- Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?arrow_forwardUse the result from Exercise 24.21 to calculate the radius of a black hole with a mass equal to: the Earth, a B0-type main-sequence star, a globular cluster, and the Milky Way Galaxy. Look elsewhere in this text and the appendixes for tables that provide data on the mass of these four objects.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_forward
- You discover by dropping particles into it that the Event Horizon (Schwartzschild Radius) of a black hole is 171 km. How massive is it? (enter just the number in solar masses)arrow_forwardUse the Schwarzchild formulaRs =2GM / c2whereRs = Radius of the star, in meters, that would cause it to become a black holeM = Mass of the star, in kilogramsG = A constant, called the gravitational constant= 6.7 x 10-11 m3 / kg . s2c = Speed of light= 3x108 meters per secondto determine to what length the radius of the Sun must be reduced for it to become a black hole. The Sun’s mass is approximately 2 x 1030 kilograms.arrow_forwardHow likely is it for a black hole to collide with Earth? Would we have much warning?arrow_forward
- How would it appear to an outside observer if someone were to enter a black hole?arrow_forward6arrow_forwardWhat is the orbital period (in s) of a bit of matter in an accretion disk that is located 6 ✕ 105 km from a 99 M black hole? Hint: Use the circular orbit velocity formula, Vc = GM r . sarrow_forward
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