The Way of Science


Cosmology and Relativity

III. Celestial "Yardsticks

Let us begin our sketch of the Universe by determining where celestial bodies are located. To do this task, we need to examine the development of longer and longer "yardsticks." Our measurements of distance are usually going to be in units called light years: that is, one ly is the distance that light travels, in a vacuum, in one year. At a speed of about 186,000 miles per second, that's about 6 trillion miles. (Warning: a ly is a unit of distance, NOT time.) Sometimes we will refer to a smaller unit, called the AU (Astronomical Unit: the distance, more or less, of the Earth to the sun, which is about 93 million miles. Converting to our light year scale, the sun is 8.5 light minutes distant. Think about that: if the Great Dragon swallowed our star right at this moment, you would not see the light vanish for over eight minutes. That's an important concept for later, and it is sometimes called "lookback time.").

To enrich your life a little bit: light slows when traveling through anything but vacuum. In water, it's only about of its vacuum speed. That's why refraction occurs, and a fish is not where it seems to be when seen from the air above. In the laboratory, light has been slowed to eight meters per second in a vapor of rubidium atoms; recently, it has been reduced to less than walking speed in the very unusual form of matter called a Bose-Einstein condensate. End of "enrich your life".

1. Triangulation
Triangulation, the first measuring technique, or "yardstick," was used by the Greeks over 2300 years ago. It is a very simple concept. Imagine the object whose distance is to be determined as located at the apex of an imaginary triangle. If we measure the length of the opposite side, plus the two angles adjacent to that side, the distance to the apex is easily computed. (Do you remember any high-school geometry or trig?) The Greeks used noon shadows cast by vertical stakes located in distant cities to make very good estimates of the distance to the sun, and the diameter of the Earth. Not bad for 2300 years ago!

One problem with any variant on triangulation is that as the object gets more distant from the observer's baseline, the harder it is to get accurate measurement of the angles. As they approach 90 degrees, and the measurement error becomes enormous, and the technique ceases to work. See the hand-outs for the illustration. The solution is to make the baseline as long as possible. A second, less obvious aid is to use parallax to help measure small changes of angle for celestial objects. Consider parallax first.

2. Parallax
Parallax is the apparent movement of an object against some unmoving background reference, when seen from two different viewing locations. We will demonstrate this phenomenon, on a small scale, in class. If you wish, try it now, as follows. Hold up a thumb a few yards in front of a wall or bookcase, and view the finger with your right eye only. Note where you thumb is on the wall. Now close that eye, open the other, and the finger appears to jump laterally, even though you held it still.

In the case of celestial objects, let's say our moon, the same technique can be used. Two distant observers simultaneously photograph the moon against the background of the distant stars. It then becomes easier to measure small angular changes.

Parallax works best with the longest possible baseline. Since the diameter of the Earth is about 8000 miles, that length would seem to be the limit on baseline length. Not so! How can one extend that baseline to millions of miles WITHOUT leaving the Earth? You already have the knowledge to answer this question for the next class. Here's a hint: think about the season and the AU.

By the early 19th century, parallax and triangulation had determined the distance to 61 Cygni (a star) as about 11 ly, and to Vega as 2.7 ly. Still, the technique began to be less and less reliable for distant objects, and the limit for any Earth-based use turns out to be about 300 ly. Alas, most celestial objects show no parallax from Earth, and thus are beyond the reach of this paltry (but critical) yardstick. Now what? Get a longer yardstick!.

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© copyright 2001, Michael Wirth and Sachiko Howard, New England College