260 The Poetry of Physics and The Physics of Poetry
For the stars of our own galaxy we see light shifted both up and
down. Some stars are moving away from us in which case the frequency
of their emission lines shift toward the red while some are moving
toward us and hence have emission lines shifted towards the blue. For
the stars of the other galaxies in our own local clusters both red and
blue shifts are also observed. For the stars of other clusters, however,
only red shifts are observed indicating that these stars are all moving
away from us.
The determination of the velocity of a star in the direction
perpendicular to the line of sight is made by measuring the change of the
angle of observation with time and knowing the distance to the star. The
transverse velocity can only be measured for nearby stars because of the
limitations of making accurate measurements of the angle of observation.
The methods of measuring distances differ for each scale of distance
measured. The methods of measuring larger distances frequently depend
on the methods of measuring smaller distances and, therefore, we begin
our survey with measurement of distance on the scale of the solar
system. The distance between Earth and Mars was determined using the
technique of triangulation. The position of Mars was observed from two
points on Earth whose distance from each other was known. By
observing the angle at which Mars appears in the sky with respect to the
distant fixed stars at the two points on Earth, one is able to determine the
triangle made by the two points on Earth and the planet Mars. One can
then determine the distance to Mars from this triangle. Once this distance
is known one can then use Kepler’s laws of planetary motion to
determine the other distances within the solar system including the
distance of the Earth from the Sun.
With the knowledge of the diameter of the Earth’s orbit about the
Sun, one can use the triangulation method to measure the distance of
nearby stars. One observes a star from the same point on Earth at
6-month intervals. The two positions of the Earth at this six-month
interval determine the base of the triangle. Measurements of the angle of
observation of the star at each of these positions enable one to complete
the triangle and determine the distance to the star. This method works for
stars up to 150 light years away. For distances greater than this, the
angles of observation cannot be measured accurately enough to make a
proper determination of the stellar distance.
For distances greater than 150 light years one must make use of
Cepheid variables, a class of stars whose luminosity varies periodically