21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 19, Problem 42QP
(a)
To determine
The amount of energy
(b)
To determine
To compare the answer obtained in subpart (a) with the energy radiated by the sun for each second.
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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.
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.
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).
Chapter 19 Solutions
21st Century Astronomy
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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- A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?arrow_forwardIn 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 laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=350,000csc(π/30*x). a. Select the graph of g(x) on the interval [0,35]. b. Evaluate g(5). Enter the exact answer. c. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? d. Find and discuss the meaning of any vertical asymptotes on the interval [0,35].arrow_forward
- a. Find the acceleration due to gravity at the surface of a neutron star of mass 1.5 solar masses and having a radius of R = 10.0 km. b. Find the weight of a 0.120-kg baseball on the surface of this star. c. Assume the equation U = mgh applies, and calculate the energy that a 70.0-kg person would expend climbing a 1.00-cm-tall mountain on the neutron star. d. Find the speed needed by a small satellite to maintain a circular orbit with a radius of 2R around the neutron 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_forwardA (relatively) nearby K-type star known as Nu? Canis Majoris has an estimated orbital radius of 2.3344 x 10° km, and an estimated orbital period of 736.9 days. a. What is the mass of Nu? Canis Majoris? b. What is the mass of Nu² Canis Majoris in terms of solar masses?arrow_forward
- What makes us think that the star system Cygnus X-1 contains a black hole? A, It emits X rays characteristic of an accretion disk, but the unseen star in the system is too massive to be a neutron star. B. No light is emitted from this star system, so it must contain a black hole. C. The fact that we see strong X-ray emission tells us that the system must contain a black hole. D.Cygnus X-1 is a powerful X-ray burster, so it must contain a black hole.arrow_forward129. In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun but occu- pying less space than our moon. Suppose that one of these black holes has a mass of 1 × 10° suns and a radius equal to one-half the radius of our moon. What is its density in grams per cubic centimeter? The mass of the sun is 2.0 × 10º kg, and the radius of the moon is 2.16 × 10° mi. (Volume of a 4 sphere =Tr.) 3arrow_forwardwhat 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_forward
- An isolated black hole in space would be difficult to detect because a. there would be no light source nearby. b. it would not be rotating rapidly. c. it would be stationary. d. very little matter would be falling into it. e. there would be very few stars behind it whose light it could block out.arrow_forwardWhat 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 kmarrow_forwardWhich statement about a rotating black hole is correct? O a. The black hole develops an ergosphere, also known as the ring of fire. O b. Inside the ergosphere, it is possible to use some of the black hole's rotational kinetic energy as an energy source. O c. The black hole's ergosphere is a location where photons can have stable orbits around the black hole. O d. The black hole begins to emit Hawking radiation when it begins to rotate. O e. The ergosphere is another name for the inner event horizon.arrow_forward
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