29:50 MODERN ASTRONOMY
Sixth Homework Set...November 5, 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 star 
Cassiopiae that I discussed in class is of spectral class G,
is at a distance of 5.95 parsecs, and has an apparent magnitude 3.4. Prove that it
is quite similar to the Sun.
Temperature same because spectral class same. From distance calculate
distance modulus to be -1.13 magnitudes. Makes M = 4.53, very similar to Sun.
(2) Assume that the Milky Way has a mass of 
solar masses, and that
its shapes can be approximated by a cylinder of radius 20 kiloparsecs and height 2
kiloparsecs. What is the mean density of the Milky Way? How does this compare with
the ``critical density'' or ``closure density'' for the universe? Reminder:
The volume of a cylinder is 
, where R is the radius and H is the height.
From data, mean density of MW = 
kg. This is to be
compared with a ``critical density'' of 
kg/m 
.
(3) Look up the distance to the Virgo cluster at the present time, either in the notes
or in the book. What was it at the time the Sun formed, 4.5 billion years ago?
About 13 Megaparsecs
(4) How long ago would the Virgo cluster and the local group have been squashed together?
About 14 billion years ago.
(5) What is the maximum age of the universe if the Hubble constant is actually 100 kilometers
per Megaparsec, as some scientists believe. Can you think of some consistency problems in
astronomy if the Hubble constant is this high?
The inferred age of the universe would be smaller than some the age of some
objects like globular star clusters.