ASTR302 Homework #4
(due in class on Wednesday, March 12, 2008)
1)
White dwarfs are held up against gravitational collapse by gas degeneracy pressure.
The equation of state gas degeneracy pressure is
3
/
5
ρ
∝
P
.
Hydrostatic equilibrium requires that
4
2
R
M
P
∝
.
a)
Use these two relations along with the definition (equation) for density to show that the
radius of a white dwarf
3
/
1

∝
M
R
.
Show your work.
b)
Do more massive white dwarf stars have larger or smaller diameters than less massive
white dwarfs?
How does this relate to the fact that the maximum mass of a white dwarf
is 1.4 solar masses?
2)
The gravitational acceleration of any object near the surface of a star or planet of mass M is
given by
g = GM/R
2
For the Earth g = 9.8 m/s
2
a)
Find g for the sun (R~10
6
km), a white dwarf (R~10
4
km), and a neutron star (R~10 km).
Let M = M
Sun
for all three.
b)
How much work would you have to do to climb a 2 cm mountain on a neutron star?
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 Winter '08
 Keller
 White dwarf, Neutron star, Compact star, gas degeneracy pressure

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