21ST CENT.AST.W/WKBK+SMARTWORK >BI<
6th Edition
ISBN: 9780393415216
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.
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 1×1021×102 suns and a radius equal to one-half the radius of our moon.
A)What is the density of the black hole in g/cm3g/cm3? The radius of our sun is 7.0×105km7.0×105km, and it has an average density of 1.4×103kg/m31.4×103kg/m3. The diameter of the moon is 2.16×1032.16×103 miles. 1km=0.6214mile1km=0.6214mile.?
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.
Chapter 19 Solutions
21ST CENT.AST.W/WKBK+SMARTWORK >BI<
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. 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_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_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_forward
- In 1999 scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun but occupying less space than our moon. Suppose that of these black holes has a mass of 1x10^3 sun's and radius equal to one-half the radius of our moon. What is the density in grams per cubic centimeter? The mass of the sun is 2.0x10^30 kg and the radius of the moon is 2.16x10^3 mi.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
- please answer c,d,earrow_forwardAn 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_forwardIf the inner accretion disk around a black hole has a temperature of 10 6 K, at what wavelength will it radiate the most energy? a. 106 nm b. 3 nm c. 3 × 106 nm d. 1 nm e. 3 × 1011 nmarrow_forward
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