Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 27, Problem 26E
Once again in this chapter, we see the use of Kepler’s third law to estimate the mass of supermassive black holes. In the case of NGC 4261, this chapter supplied the result of the calculation of the mass of the black hole in NGC 4261. In order to get this answer, astronomers had to measure the velocity of particles in the ring of dust and gas that surrounds the black hole. How high were these velocities? Turn Kepler’s third law around and use the information given in this chapter about the galaxy NGC 4261-the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas-to calculate how long it would take a dust particle in the ring to complete a single orbit around the black hole. Assume that the only force acting on the dust particle is the gravitational force exerted by the black hole. Calculate the velocity of the dust particle in km/s.
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The Schwarzschild radius is the distance from an object at which the escape velocity is equal to the speed of light. A black hole is an object that is smaller than its Schwarzschild radius, so not even light itself can escape a black hole. The Schwarzschild radius r depends on the mass m of the black hole according to the equation
(See image.)
where G = 6.673 × 10-11 (Nm2)/(kg2) is the gravitational constant and c = 2.998 × 108 m/s is the speed of light.
1. Consider a black hole with a mass of 3.70 × 107M.. Use the given equation to find the Schwarzschild radius for this black hole. Remember that 1 M = 1.989 × 1030 kg and 1 N = 1 kg * m/s2
2. What is this radius in units of the solar radius? Remember that 1 R = 6.955 × 108 m.
Supermassive black holes are thought to exist at the center of many galaxies. What is the radius of such an object if it has a mass of 109 Suns?
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.
Chapter 27 Solutions
Astronomy
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Ch. 27 - What evidence do we have that the luminous central...Ch. 27 - Suppose you observe a star-like object in the sky....Ch. 27 - Why don’t any of the methods for establishing...Ch. 27 - One of the early hypotheses to explain the high...Ch. 27 - A friend of yours who has watched many Star Trek...Ch. 27 - Could the Milky Way ever become an active galaxy?...Ch. 27 - Why are quasars generally so much more luminous...Ch. 27 - Suppose we detect a powerful radio source with a...Ch. 27 - A friend tries to convince you that she can easily...Ch. 27 - Show that no matter how big a redshift (z) we...Ch. 27 - If a quasar has a redshift of 3.3, at what...Ch. 27 - If a quasar is moving away from us at v/c=0.8 ,...Ch. 27 - In the chapter, we discussed that the largest...Ch. 27 - Rapid variability in quasars indicates that the...Ch. 27 - Large redshifts move the positions of spectral...Ch. 27 - Once again in this chapter, we see the use of...Ch. 27 - In the Check Your Learning section of Example...Ch. 27 - In the Check Your Learning section of Example...Ch. 27 - The quasar that appears the brightest in our sky,...
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