29:50 MODERN ASTRONOMY
Seventh Homework Set...November 29, 1999
Note: Having problems? Don't go around confused and despondent! Ask for help! The purpose
of these problem sets is to help you learn something.
(1) The number density of molecules in the Earth's atmosphere at ground level is about
. These molecules are mainly diatomic (two atoms in
each molecule) molecules of Nitrogen with about 20 % Oxygen. Roughly how much less dense
is the mean number of atoms in the universe? Hint: Think about the value of the
critical density for a closed universe, and how the true density of the universe compares
with that value.
28 orders of magnitude, i.e. a factor of 
(2) The Cosmic Background Radiation, leftover from the Big Bang, has a spectrum
which is that of Blackbody radiation with a temperature of 3 K. At what wavelength is this
radiation brightest?
meters
(3) An asteroid orbits the Sun in a orbit with a semimajor axis of 2.5 astronomical units.
How long does it take to complete its orbit around the Sun?
3.95 years
(4) A comet move on an orbit with a perihelion, or point of closest approach to the
Sun, of 1.0 astronomical units, and an aphelion, or point of greatest distance from
the Sun, of 15 astronomical units. What is its orbital period?
22.6 years
(5) Look at the orbit in Figure 4.15 on p63 of your textbook. What is the eccentricity of
the orbit?
about 0.70
(6) Do problem 16, page 69 of your textbook.
au
(7) About 15 years ago, there was a flurry of speculation about an object called the
Death Star, an object with an alleged orbital period of 25 million years. This number
was derived because some scientists believed there was weak evidence for a 25 million year
periodicity in major extinctions on Earth. What would be the semimajor axis of such an
object? Assuming that it had a perihelion in the inner solar system (so it could kill off
ammonites and dinosaurs, etc), how far would it be from the Sun at maximum distance? Using
what else you have learned in this course, does anything strike you as odd about this
number?
Figure it out!
(8) A radioistope A decays to isotope B 
with a half life of
5 billion years. Space scientists find a type of rock on Europa which which only contains
the element of which A is an isotope. In other words, this rock would have formed with
zero atoms of isotope B. When an analysis on the rock is formed, it is found to have
750 atoms of B per cubic centimeter, and 250 atoms of A. How old is this rock? Is your
number consistent with other information you have learned in this course?
10 billion years. Too old.
(9) Look at pictures of Jupiter's moon Europa on pages 310 and 311 of your textbook. Using
what we know about lunar geological history, what would you conclude about the
geological history of Europa?
The ice froze in the recent geological past, or at least well after age of
bombardment.