FUND. OF PHYSICS FOR LSU WILEY+ NEXT GEN
11th Edition
ISBN: 9781119749295
Author: Halliday
Publisher: WILEY
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Chapter 44, Problem 39P
To determine
To:
(a) show that to prevent unlimited expansion of the universe, its average density must at least be equal to
(b) evaluate the ‘critical density’ numerically in terms of H-atoms per cubic meters.
.
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*39 Will the universe continue to expand forever? To attack this
question, assume that the theory of dark energy is in error and that
the recessional speed v of a galaxy a distance r from us is determined
only by the gravitational interaction of the matter that lies inside
a sphere of radius r centered on us. If the total mass inside this
sphere is M, the escape speed v, from the sphere is v. = V2GMIT
(Eq. 13-28). (a) Show that to prevent unlimited expansion, the aver-
age density p inside the sphere must be at least equal to
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(b) Evaluate this "critical density" numerically; express your an-
swer in terms of hydrogen atoms per cubic meter. Measurements
of the actual density are difficult and are complicated by the pres-
ence of dark matter.
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.
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 44 Solutions
FUND. OF PHYSICS FOR LSU WILEY+ NEXT GEN
Ch. 44 - Prob. 1QCh. 44 - Prob. 2QCh. 44 - Prob. 3QCh. 44 - Prob. 4QCh. 44 - Prob. 5QCh. 44 - Prob. 6QCh. 44 - Prob. 7QCh. 44 - Prob. 8QCh. 44 - Prob. 9QCh. 44 - Prob. 10Q
Ch. 44 - Prob. 11QCh. 44 - Prob. 1PCh. 44 - Prob. 2PCh. 44 - Prob. 3PCh. 44 - Prob. 4PCh. 44 - Prob. 5PCh. 44 - Prob. 6PCh. 44 - Prob. 7PCh. 44 - GO A positive tau , rest energy = 1777 MeV is...Ch. 44 - Prob. 9PCh. 44 - Prob. 10PCh. 44 - Prob. 11PCh. 44 - Prob. 12PCh. 44 - Prob. 13PCh. 44 - Prob. 14PCh. 44 - Prob. 15PCh. 44 - Prob. 16PCh. 44 - Prob. 17PCh. 44 - Prob. 18PCh. 44 - Prob. 20PCh. 44 - Prob. 21PCh. 44 - Prob. 22PCh. 44 - Prob. 23PCh. 44 - Prob. 24PCh. 44 - Prob. 25PCh. 44 - Prob. 26PCh. 44 - Prob. 27PCh. 44 - Prob. 28PCh. 44 - Prob. 29PCh. 44 - Prob. 30PCh. 44 - Prob. 31PCh. 44 - Prob. 32PCh. 44 - Prob. 33PCh. 44 - Prob. 34PCh. 44 - Prob. 35PCh. 44 - What would the mass of the Sun have to be if Pluto...Ch. 44 - Prob. 37PCh. 44 - Use Wiens law see Problem 37 to answer the...Ch. 44 - Prob. 39PCh. 44 - Prob. 40PCh. 44 - Prob. 41PCh. 44 - Due to the presence everywhere of the cosmic...Ch. 44 - SSM Suppose that the radius of the Sun were...Ch. 44 - Prob. 44PCh. 44 - Prob. 45PCh. 44 - Prob. 46PCh. 44 - Prob. 47PCh. 44 - Prob. 48PCh. 44 - Prob. 49PCh. 44 - Prob. 50PCh. 44 - Prob. 51PCh. 44 - Prob. 52PCh. 44 - Prob. 53PCh. 44 - Prob. 54P
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