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Homework Handout #10

**10.01: (a) A white dwarf has an apparent magnitude ***m*_{V}
= 8.5 and parallax p = 0.2". Its bolometric
correction is -2.1 mag, and *T*_{eff} = 28,000 K. Assume
*A*_{V}
= 0. Calculate the radius of the star. Compare your value with
the radius of the Earth.
**10.02: Consider stars of mass 1 ***M*_{o}. Compute
the mean mass density for the following: (a) our Sun (*R*_{o}
= 7 x 10^{5} km), (b) a white dwarf (*R* = 10^{4}
km), (c) a neutron star (*R* = 10 km). Now consider a ^{12}C
nucleus of radius *r* = 3 x 10^{-15} m and compute its mean
density. Discuss the significance of these results.

**10.03: The Crab Nebula pulsar radiates at a luminosity of about 1
x 10**^{31} W and has a period of 0.033 s. If *M* = 1.4
*M*_{o}
and *R* = 1.1 x 10^{4} m, determine the rate at which its
period is increasing (*dP/dt*). How many years will it take
for the period to double its present value? (*Hint:* You must integrate
after isolating all the terms involving *P* on the left-hand side
for the latter calculation.)

**10.04: Assume a brown dwarf's luminosity derives from gravitational
contraction. Its mass is 0.05 ***M*_{o}, and its luminosity
is 3 x 10^{-5} *L*_{o}. If we assume that its
luminosity has been constant (even when the star has a much larger radius),
how long can a star of this type radiate before the contraction is halted
by electron degeneracy pressure (when *R* = 9 x 10^{6} *M
*^{-1/3}
m, where *M* is in solar units)?