10.02: Consider stars of mass 1 Mo. Compute the mean mass density for the following: (a) our Sun (Ro = 7 x 105 km), (b) a white dwarf (R = 104 km), (c) a neutron star (R = 10 km). Now consider a 12C 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 1031 W and has a period of 0.033 s. If M = 1.4 Mo and R = 1.1 x 104 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 Mo, and its luminosity
is 3 x 10-5 Lo. 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 106 M
m, where M is in solar units)?