Inquiry into Physics
8th Edition
ISBN: 9781337515863
Author: Ostdiek
Publisher: Cengage
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Chapter 12, Problem 19Q
To determine
Whether the pulsating stars contraction and expansion, due to thermal instabilities in their atmosphere, generate gravitational waves or not.
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Suppose a star 1000 times brighter than our Sun (that is, emitting 1000 times the power) suddenly goes supernova. Using data from Table: (a) By what factor does its power output increase? (b) How many times brighter than our entire Milky Way galaxy is the supernova? (c) Based on your answers, discuss whether it should be possible to observe supernovas in distant galaxies. Note that there are on the order of 1011 observable galaxies, the average brightness of which is somewhat less than our own galaxy.
Problem 2: Black hole – the ultimate blackbody
A black hole emits blackbody radiation called Hawking radiation. A black hole with mass
M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of
hc³/167²KGM.
a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar
mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole.
b) Calculate the total power radiated by a one-solar mass black hole.
c) 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 "evaporates". Derive a
differential equation for the mass as a function of time, and solve to obtain an
expression for the lifetime of a black hole in terms of its mass.
Another commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is
the minimum velocity a star must have in order to escape the gravitational field of the galaxy.
(a) Starting from the work required to move a body over a distance dr against f show that
the escape velocity from a point mass galaxy is vsc = 2GM/r where r is your initial distance.
(b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a
galaxy with a p(r) xr¯² density profile is vese
that R is a cutoff radius at which the mass density is zero.
= 2v(1+ ln(R/r)). Here you must assume
(c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc,
is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in
kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the
galaxy. Note the solar rotation velocity is 220 km/s.
Chapter 12 Solutions
Inquiry into Physics
Ch. 12 - Prob. 1AACh. 12 - Prob. 2AACh. 12 - Prob. 1PIPCh. 12 - Prob. 1MIOCh. 12 - Prob. 2MIOCh. 12 - Prob. 1QCh. 12 - Prob. 2QCh. 12 - Prob. 3QCh. 12 - Prob. 4QCh. 12 - Prob. 5Q
Ch. 12 - Prob. 6QCh. 12 - Prob. 7QCh. 12 - Prob. 8QCh. 12 - Prob. 9QCh. 12 - (Indicates a review question, which means it...Ch. 12 - Prob. 11QCh. 12 - Prob. 12QCh. 12 - (Indicates a review question, which means it...Ch. 12 - Prob. 14QCh. 12 - Prob. 15QCh. 12 - Prob. 16QCh. 12 - Prob. 17QCh. 12 - Prob. 18QCh. 12 - Prob. 19QCh. 12 - Prob. 20QCh. 12 - Prob. 21QCh. 12 - Prob. 22QCh. 12 - Prob. 23QCh. 12 - Prob. 24QCh. 12 - Prob. 25QCh. 12 - Prob. 26QCh. 12 - Prob. 27QCh. 12 - Prob. 28QCh. 12 - Prob. 29QCh. 12 - Prob. 30QCh. 12 - Prob. 31QCh. 12 - Prob. 32QCh. 12 - Prob. 33QCh. 12 - Prob. 34QCh. 12 - Prob. 35QCh. 12 - Prob. 36QCh. 12 - Prob. 37QCh. 12 - Prob. 38QCh. 12 - Prob. 39QCh. 12 - Prob. 40QCh. 12 - Prob. 41QCh. 12 - Prob. 42QCh. 12 - Prob. 43QCh. 12 - Prob. 44QCh. 12 - Prob. 1PCh. 12 - How fast would a muon have to be traveling...Ch. 12 - The lifetime of a free neutron is 886 s. If a...Ch. 12 - Prob. 4PCh. 12 - The formula for length contraction gives the...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - . In a particular beam of protons, each particle...Ch. 12 - . A particle of rest energy 140 MeV moves at a...Ch. 12 - . If the relativistic kinetic energy of a particle...Ch. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - . How many years would you have to wait to observe...Ch. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - . A compact neutron star has a mass of kg (about...Ch. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Prob. 28PCh. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - . If the average lifetime of a proton was 1033...Ch. 12 - Prob. 1CCh. 12 - Prob. 2CCh. 12 - Prob. 3CCh. 12 - Prob. 4CCh. 12 - Prob. 5CCh. 12 - Prob. 6CCh. 12 - Prob. 7CCh. 12 - Prob. 8CCh. 12 - Prob. 9CCh. 12 - Prob. 10C
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- Please mention all theory parts.arrow_forwardModels of the first star-forming clouds indicate that they had a temperature of roughly 150 K and a particle density of roughly 400,000 particles per cubic centimeter at the time they started trapping their internal thermal energy. ▼ Part A Estimate the mass at which thermal pressure balances gravity for these values of pressure and temperature. Express your answer in kilograms. —| ΑΣΦ Mcloud Submit Part B = Mcloud How does that mass compare with the Sun's mass? Express your answer in solar masses. Submit Request Answer = ΤΙ ΑΣΦ Request Answer ? ? kg MSun Reviewarrow_forwardFor the Galactic Center black hole (Sag. A*), which has mass ~4.1 million solar masses, find the maximum luminosity that could be emitted via spherical accretion of ionized gas (i.e., the Eddington limit LEdd). Express your answer as a multiple of the Qmlaxy's total luminous output, = 2.5 x 1010 L. LMW (i.e., enter the ratio LEdd/LMw).arrow_forward
- Another commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vse = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a galaxy with a p(r) x r-² density profile is vse = 2v²(1+ ln(R/r)). Here you must assume that R is a cutoff radius at which the mass density is zero. (c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc, is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the galaxy. Note the solar rotation velocity is 220 km/s.arrow_forwardPlease provide Given, Required, and Solution. Thanks!arrow_forwardEZ GWS. A neutron star collision produced gravitational waves passing through Earth's detectors at the starting frequency of f = 24[Hz]. If the wave travelled at the speed of light (v = 300 000 [km/s]), what is the wavelength of the gravitational wave (assuming it follows simple wave quantities)? Select one: O 12500 [m] O 8000[km] O 12500[km] O 7200[m]arrow_forward
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