Homework 3 solutions

1) We can think of a thin gas as a collection of individual atoms.  We
learned, from studying the Bohr atom, that electrons have certain
quantized possible energy states. To jump from one energy state to
another, the electron must absorb (or emit) light of a specific energy
(wavelength,frequency). All other energies of light are not able
to be absorbed (emitted) by the atom.

So, when you shine light of all colors at a thin gas, the energies
(colors) that are able to be absorbed (because the energies are just
right) are absorbed, and the rest pass unimpeded to the observer. The
observer sees light of all colors minus the absorbed colors (lines).

2) To do this problem, you need to look at a couple of H-R diagrams
posted on the web.


http://adansonia.as.arizona.edu/~edo/astro203_fall2003/figures_directory/sept11/impey17_2.jpg

and

http://adansonia.as.arizona.edu/~edo/astro203_fall2003/figures_directory/sept11/impey17_8.jpg

It's best to print them out so that you can use a ruler.

2a) Lifetime =(lifetime of sun) TIMES (mass of star in solar masses) DIVIDED BY
(luminosity of star in solar units)

This is the same as 
Mileage per fillup = (miles per fillup in a volkswagon) TIMES (size of fuel tank
in units of volkswagon fuel tanks) TIMES (miles per gallon in units of
volkswagon miles per gallon)

So, if a volkswagon gets 300 miles per fillup and has a 10 gallon tank
and gets 30 miles per gallon, and if a corvette has a 20 gallon tank
and gets 10 miles per gallon

Corvette miles = 300 TIMES (20/10) TIMES (10/30) = 300 TIMES 2 TIMES 1/3 = 200
miles

A corvette has a bigger gas tank but travels a smaller distance per fillup.


Ok, so reading from figure 17_5, we get that a 3000 degree star has
a luminosity of .001 solar luminosities.

From the other figure, we get that this same star has a mass of around 0.1-0.2
solar masses (we'll use 0.1 here)

So lifetime= (10**10) TIMES (0.1/1) DIVIDED BY (.001/1)= 10**12 years.

2b) (1x10**12)/1.5x10**10) = 70 current universe ages
     I MADE A MISTAKE IN THE HOMEWORK, it's 1.5x10**10, not 15x10**10,
     but we won't hold it against you. (age of universe is 15 billion years)
     So using the numbers I gave, you'll have gotten 7 current universe ages.

2c) Mass we already know, about 0.1 solar masses
    Radius is about .005 solar radii.

2d) Yup, it's a trick question. As you know from thinking about yourself,
lifetime does not equal age.

The only stars for which we can say lifetime equals age is for really
massive stars whose lifetime is so short that to a reasonable
approximation the lifetime and any age are the same number. If "the
Mayfly lives but a day or so", then if you see a Mayfly it's about 1
day old and will live for about a day in total. If a turtle lives 150
years and you see a turtle, it can be anywhere between a few years old
and 150 years old.

So astronomers must have other ways than we've learned to date, to tell ages.

3) If you ask the question "when Nature makes 100 stars, how does she
distribute their masses", you can test this by catching a bunch
of 100-star samples in a bunch of boxes. One such box is the sample
of the 100 stars closest to the Sun. Most stars are fainter and cooler
than the Sun because that's how Nature chooses to make them. Hot, luminous 
stars are very rare so you need really big boxes to catch one.

So we're missing these stars because they're so rare that they won't be
in small samples. (Another way of thinking about this problem is
that the stars we see in the night sky is not a representative
sample, it's warped because of the huge range in luminosities
in the H-R diagram. Another way of thinknig about this idea is
that the nearest star to the Sun, PROXIMA CENTAURI, is not
visible to the naked eye.)

4) Potassium 40 is the radioactive element. Because it's being destroyed
there is less potassium 40 over time. Argon 40 is made from the decay
of potassium 40. So as potassium 40 is destroyed, argon 40 is created.
The sum of the two is a constant, since argon 40 is being made from potassium
40. The ratio of the two depends on the age of the rock. A young rock
will have mostly potassium 40 while an old rock will have mostly
argon 40.