21st Century Astronomy (sixth Edition)
6th Edition
ISBN: 9780393675504
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton & Company
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Chapter 19, Problem 40QP
To determine
The amount of energy released by the dying star.
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A black hole is a blackbody if ever there was one, so it should emit blackbody radiation, called Hawking radiation. A black hole of mass M has a total energy of MC2, a surface area of 16πG2M2 / c4 and a temperature of hc3 /16π2kGM.
Imagine a black hole in empty space, where it emits radiation but absorbs nothing. As it loses energy, its mass must decrease; one could say it "evaporates." Derive a differential equation for the mass as a function of time, and solve this equation to obtain an expression for the lifetime of a black hole in terms of its initial mass.
In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.
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Chapter 19 Solutions
21st Century Astronomy (sixth Edition)
Ch. 19.1 - Prob. 19.1ACYUCh. 19.1 - Prob. 19.1BCYUCh. 19.2 - Prob. 19.2CYUCh. 19.3 - Prob. 19.3CYUCh. 19.4 - Prob. 19.4CYUCh. 19 - Prob. 1QPCh. 19 - Prob. 2QPCh. 19 - Prob. 3QPCh. 19 - Prob. 4QPCh. 19 - Prob. 5QP
Ch. 19 - Prob. 6QPCh. 19 - Prob. 7QPCh. 19 - Prob. 8QPCh. 19 - Prob. 9QPCh. 19 - Prob. 10QPCh. 19 - Prob. 11QPCh. 19 - Prob. 12QPCh. 19 - Prob. 13QPCh. 19 - Prob. 14QPCh. 19 - Prob. 15QPCh. 19 - Prob. 16QPCh. 19 - Prob. 17QPCh. 19 - Prob. 18QPCh. 19 - Prob. 19QPCh. 19 - Prob. 20QPCh. 19 - Prob. 21QPCh. 19 - Prob. 22QPCh. 19 - Prob. 23QPCh. 19 - Prob. 24QPCh. 19 - Prob. 25QPCh. 19 - Prob. 26QPCh. 19 - Prob. 27QPCh. 19 - Prob. 28QPCh. 19 - Prob. 29QPCh. 19 - Prob. 30QPCh. 19 - Prob. 31QPCh. 19 - Prob. 32QPCh. 19 - Prob. 33QPCh. 19 - Prob. 34QPCh. 19 - Prob. 35QPCh. 19 - Prob. 36QPCh. 19 - Prob. 37QPCh. 19 - Prob. 38QPCh. 19 - Prob. 39QPCh. 19 - Prob. 40QPCh. 19 - Prob. 41QPCh. 19 - Prob. 42QPCh. 19 - Prob. 43QPCh. 19 - Prob. 44QPCh. 19 - Prob. 45QP
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- Astrophysical theory suggests that a burned-out star whose mass is at least three solar masses will collapse under its own gravity to form a black hole. If it does, what is the radius of its event horizon?arrow_forwardHow massive would a black hole have to be to have an event horizon the same size as the Earth? Assume the Earth's radius is 6,300 km. Answer in solar masses.arrow_forwardA spaceship is located around 2.6×10¹³ km from the black hole Messier 87. It has a mass of 6.6 billion suns. How long will their day last compared to a day on Earth?arrow_forward
- 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 “The Sun is _____ times smaller/bigger than the black hole.”arrow_forwardA gravitational dead zone is found between two hyper giant stars, HG A and HG B, 34 million km from HG A. It is known that the mass of B is 25 x the mass of A. Determine the distance between the two stars in millions of km.arrow_forwardHow close, r, to the center of a neutron star would a manned satellite be orbiting if it were at the location where the gravitational force from the star equaled the gravitational force of the Earth's surface? RN = neutron star radius = 1 × 104 kmM N = neutron star mass = 3 × 1030 kgG = universal gravitational constant = 6.67 × 10-11 N m2 / kg2g⊕ = Earth gravitational acceleration = 9.807 m/s²arrow_forward
- In 1999, scientists discovered a new class of black holes with masses 100 to 10000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5km and it has an average density of 1.4x10^3kg/m^3. The diameter of the moon is 2.16x10^3 miles. Note: the volume of a sphere is V=4/3 pie r^3arrow_forwardA Doppler redshift in light from a star indicates that the star is_____.arrow_forwardThe 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.arrow_forward
- What would you have to do to make earth a black hole ?arrow_forwardWhat must be the radius of a star of mass 2 x 10^30 kg so that the escape speed from this star is equal to 2 × 10^8 m/s?arrow_forwardA light of wavelength 620 nm is emitted from the following four places. What wavelength is observed for this light by an observer a long distance away? (The objects are not moving with respect to the observer) The surface of a 0.84 solar mass white dwarf that has a radius of 708000 km: ? The surface of a 2.52 solar mass neutron star that has a radius of 14.2 km: 2 Schwarzschild radii from a 20 solar mass black hole: ? 1.048 Schwarzschild radii from a 20 solar mass black hole: ?arrow_forward
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