10.02: Consider stars of mass 1 M_o.  Compute the mean mass density for the following: (a) our Sun (R_o = 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 M_o 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 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 10⁶ M ^-1/3 m, where M is in solar units)?