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Section I: Introduction
Section II: 6 Activities
Section III: Summary

Education Activities To Accompany Chandra Data Analysis Software

The Time Machine


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.

  1. Now, position the lamps next to each other, and stand about ten feet away from both of them. Which appears brighter? Why?
  2. 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
  3. 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:
    1. different sizes of punched holes for each lamp and
    2. 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]

Last updated: 03/21/08


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