AST 301
Homework #6
Due Friday March 7
1. Look up the diameter of the Sun and the size of the Astronomical Unit (AU) in your book. When the Sun becomes a
red giant, in about 5 billion years, its diameter will increase to about 1 AU.
a) By what factor will the diameter of the Sun change?
(How many times larger will it be?)
b) By what factor will the radius of the Sun change?
c) By what factor will the surface area of the Sun change?
d) If the temperature of the Sun didn't change while becoming a red giant, it would become more luminous simply because
it would have a larger surface to radiate light.
If the temperature of the Sun didn't change while it diameter increased to 1 AU, by what factor would its luminosity change?
e) In fact, the surface of the Sun will cool from about 6000 K to about 3000 K when it becomes a red giant. By what factor
will the power radiated by each square meter of its surface change? (We haven't talked about this formula in class. You will have to find it in the book.)
f) Now, combine your answers to parts e and f to calculate what the luminosity of the Sun will be when it becomes a red giant.
2. a) Make a table with 4 columns. Label the columns Temperature, Luminosity, Mass, and Lifetime.
b) Choose 3 main sequence stars and 2 red giants from Figure 8-20 in your book. Read their temperatures, luminosities, and
masses from the figure and enter them on 5 lines in your table.
c) Using the fact that the main-sequence lifetime of the Sun is about 1010 years and the idea that the lifetime of a star is
proportional to the ratio of its mass to its luminosity
(that is, the ratio of the amount of fuel it has to the rate at which it burns it), calculate the lifetime of each star
in your table. (This calculation won't be quite right for the red giants since they are burning different fuels, but it
should tell you that stars don't stay red giants for as long as they stay main-sequence stars.)
|
