ASTR 1040 Spring, 2005 1.a. Estimate the hydrogen-burning
lifetime of a star of 15 solar masses and a luminosity 10,000
times greater than the solar luminosity. This is easiest to do
by comparing with the Sun, using the relationship t = to(M/L),
where t_o is the Sun's lifetime of 10^10 years, and M and L are
the mass and luminosity of the star, in solar units. Then we get
t = 10^10(15/10,000) = 1.5 X 10^7 yrs. b. For a star having a
mass of 0.2 M_o and a luminosity of 0.008 L_o, Using the same
method yields t = 10^10(0.2/0.008) = 2.5 X 10^11 yrs. c. If 10
percent of the star's original mass is now in the form of helium
in the core, calculate the helium-burning lifetime of the
15-solar mass star. The mass converted to energy is the
difference between the sum of the masses of three helium nuclei
(i.e. 3 X 4.002603 u = 12.007809 u) and the mass of the
resulting carbon nucleus (12.000000 u), which is 0.007809 u.
This represents a fractional loss of mass of 0.007809/12.007809
= 0.00065 of the original mass. Thus 0