Homework 3: Properties of Stars
(due at the start of class November 18, 2003)
1. Referencing the internet or any other suitable resource, write a paragraph
describing one of the following three topics:
a. The solar neutrino problem.
b. Supernova 1987A.
c. The GAIA mission.
Be sure to describe why the topic is interesting, and, if applicable, report on any
recent developments related to the topic.
2. The starship Nemesis enters orbit around a distant blue star. Use the following
equations to work out the problems below:
Newton’s form of Kepler’s 3rd Law: (Distance)3  Mass  (Period)2 .
Stephan-Boltzmann Law: Luminosity  (Radius)2  (Temperature)4 .
a. It takes Nemesis 2 yr to orbit the star at a distance of 5 AU. What is the
mass of the star, in units of our Sun’s mass (M)? Show your work.
b. Nemesis measures the star’s radius to be 10 R (i.e., 10 times larger than
one solar radius) and its surface temperature to be 9.5 T. What is the
star’s luminosity? Show your work. Is your answer reasonable
considering what you found for the star’s mass in part a? Hint: most stars
follow the “mass-luminosity” relation, Luminosity  (Mass)4.
c. What is the likely fate of this star? I.e., will it become a white dwarf,
neutron star, or black hole?
3. Estimate the expected lifespan of the Sun, assuming all its hydrogen is consumed
by fusion and that its luminosity (energy released per unit time) is constant at L
= 3.85  1026 W (in reality, the Sun’s luminosity increases over time as it burns
hydrogen in its core). Show your work and express your answer in Gyr. Use the
fact that the Sun started with roughly 1.5  1030 kg of hydrogen and that for every
kg of hydrogen consumed during fusion, 0.7% is liberated in the form of pure
energy via the equation E = mc2, where m is the mass and c = 3  108 m s-1 is the
speed of light. Your answer should be quite a bit larger than the Sun’s actual
lifetime of about 10 Gyr. What do you suppose is the reason for this difference?