Education Activities To Accompany Chandra Data Analysis Software 3C273
The Time Machine
Introduction
One of the most remarkable and useful
characteristics of our universe is that as we look out into space, we
are also looking backward in time. Since light travels about 186,000
miles in one second, when we look at the Sun whose distance is about
93,000,000 miles, we are seeing it as it was about 8 minutes ago. Thus,
our astronomical observations can yield a history of our universe by
examining objects very far away.
However, we had no idea of the vastness and hence antiquity of
the universe until the 1920's, when Edwin Hubble discovered some
innocuous appearing stars in a "nebula" (cloud) called M31. These
objects were Cepheid variable stars, which have the unique feature that
they pulsate, actually growing and shrinking over a period of several
days. Moreover, the amount of time it takes for these stars to pulsate
is directly related to their intrinsic luminosity, how bright they really are. Once we know an object's true brightness, it is a simple matter to use its apparent
brightness to calculate its distance from us. It was undoubtedly with a
trembling hand that Hubble calculated the distance to M31, our nearest
spiral galaxy neighbor; over 1 million light years away. Just imagine,
light that can travel over 7 times around the world in one second,
takes over a million years to reach us from M31. Thus, when you go out
on a clear autumn night, and find M31 in the constellation of
Andromeda, you are seeing the object as it actually was when the first
human-like creatures began to walk the Earth.
Activity 1a: Understanding brightness and calculating distance.
An important tool for understanding
the intrinsic and apparent brightness of astronomical objects is the
inverse square law for light. Try this experiment: Obtain two desk
lamps, that are surrounded by metal shades. Place a 25W bulb in one,
and a 100W bulb in the other. Carefully punch a small hole in each of
two pieces of tin foil, and place these over the open end of each of
the shades so that you are only seeing a small pin-hole of light
emerging from each lamp.
Now, position the lamps next to each other, and stand about ten feet away from both of them. Which appears brighter?
Why?
Moving the fainter appearing
light, try to find a position where they appear equally luminous. If
the inverse square law holds, where would you expect to see equal
brightnesses? Click Here for the Solution Click Here for Detailed Hints
If you've done this experiment without cheating (!), you will find that the 25W bulb will not
appear equal in brightness at exactly the half way point. Why?
[Understanding the sources of error in an observation is absolutely
vital in figuring out what is really going on. By examining this simple
experiment, you can obtain a first-hand look at the problems scientists
face in interpreting results. Among the sources of error in our
experiment might be:
different sizes of punched holes for each lamp and
different amounts of energy
emitted by each bulb in the "invisible" parts of the spectrum such as
the infra-red and ultra-violet. [Can you think of others? Can you think
of some simple ways you can compensating for these "errors"?]
With the knowledge of the distance to
far flung astronomical bodies, a wonderful side benefit emerged: we are
able to find the dimensions of an object from its angular size in the
sky. We do this exercise with Cas-A.
Activity 1b: What is the size of the Andromeda galaxy, M31?
Here, we'll calculate the size of M31. Assuming that it is
about 2 million light years away, and its apparent size in the sky is
3 degrees (about the same apparent diameter as 6 full moons, placed
side by side), what is the size of the Andromeda Galaxy?
Click Here for the Solution Click Here for Detailed Hints
With this awesome revelation about the size of the universe and
some of its constituents, an avalanche of observations opened our eyes
to yet more astounding facts. With the study of other galaxies, an
exceedingly interesting relationship emerged. The further a galaxy was
away from us (measured by the Cepheid variables and other techniques),
the faster it appeared to be moving away from us (as measured from the
Doppler shift of its spectral features). It was as if the entire
Universe was somehow exploding into space; the faster each piece was
moving, the further it would be away from anywhere else, after a given
amount a time.
Because of this unique relationship between velocity and
distance (now known as the Hubble law, in honor of its discoverer), we
now had a new method for measuring distances to really remote objects.
All we need to do is measure their red-shift from the energy spectrum,
and deduce the distance from v=Hr (where H is the Hubble constant and
has been experimentally determined to be about 50 km/sec/Mpc, and r is
distance). Thus, for each million parsecs in distance away from us
(about 3 million light-years), the object's velocity increases by about
50 km/sec. So an object whose spectrum exhibits a velocity of 500
km/sec would be at a distance of about 10 Mpc from us).
The stage was now set for the discovery of the quasars [next] [back]
