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Introduction to Astrophysics 0321.3108
Problems Set
1. The virial theorem states that for a star in hydrostatic equilibrium
< P >
=

1
3
E
gr
V
, where
< P >
is the volume average pressure,
V
is the volume, and
E
gr
is the gravitational potential
energy.
a.
For a star supported by thermal gas pressure
P
=
nk
B
T
, what is the relationship between
the internal energy
E
K
and
E
gr
.
b.
Assume the Sun is supported by thermal gas pressure and is composed entirely of ionized
hydrogen. Estimate the typical (virial) temperature
< T >
in the Sun.
c.
For a star dominated by radiation pressure, what is the relationship between
E
k
and
E
gr
?
What is the total
E
tot
in this case?
d.
Find an expression for the mass of a star at which radiation pressure begins to domi
nate. Don’t worry about numerical factors, express your answer in terms of the physical
constants
c, h, G
and
m
H
.
2.
KelvinHelmholtz time
Derive an expression for the Kelvin Helmholtz time for which the
Sun could be shining at its present luminosity due to the release of gravitational energy.
Calculate this time in years.
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 Spring '10
 Sternberg
 Physics, Energy, Potential Energy, Static Equilibrium

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