DISTANCE TO THE PLANETS AND STARS

The early Greek astronomers had no way of estimating the distance to the stars, and assumed that they were all at the same distance, beyond the most-distant planet. In the Ptolemaic model, the most highly developed Greek cosmology (which remained the "standard" cosmology until the time of Copernicus), that planet was Saturn at a distance of about 75 million miles. This distance estimate was based on the idea that the planets were attached to tightly-nested spheres, with no empty space between the outer edge of a planet and the inner edge of the neighboring planet. Using Aristarchus' estimate of the Earth-Sun distance plus estimates of the sizes of the planets, Ptolemy arrived at a planetary system that was way too small (by a factor of 10) compared with modern values, but still huge compared with the distance scales of the time.

THE PARALLAX VIEW

With the acceptance of the idea of a moving Earth orbiting the Sun, it became possible to reconsider the notion that the stars are all at the same distance from the center of the Universe (the Sun in the Copernican model). In any moving-Earth model, it is possible that the movement of the Earth will lead to an apparent annual motion of the stars known as the "stellar parallax ". Parallax is simply the change in the apparent position of a nearby object relative to a more-distant object due to a change in the position of the observer. It can easily be demonstrated by extending your arm and looking at your thumb first with one eye and then with the other. (Parallax is interpreted by your brain to construct "depth-perception"). An interactive illustration for the stellar case is available on the web. If the Earth moves and parallax shifts are not observed from one side of its orbit to another, then either the stars are all exactly at the same distance from the Sun, or they are so far away that the shifts are too small to observe. In fact, stellar parallax was finally observed around 1838 by Bessel, Struve, and Henderson. The largest known stellar parallax, 0.76 seconds of arc, was measured by Henderson for the star alpha-Centauri. This places it at a distance of about 270,000 times the Earth-Sun distance, or 25 million million miles. This is therefore the closest star to us, and the scale of the Universe is clearly immense. Even more remarkably, only about a thousand of all the known stars are close enough that their parallax can be measured, even with the most modern instruments. Because of the very large distances implied by these measurements, astronomical distances are often measured in "parsecs". One parsec is the distance at which a star would have a parallax of one second of arc, i.e., about 19 million million miles. Another commonly used distance unit is the "light-year". One light-year is the distance that light, traveling at about 186,000 miles per second, covers in one year. On this scale, the distance to alpha-Centauri is 4.3 light-years, and one parsec is the equivalent of about 3.3 light-years.

PARALLAX RE-VISITED: CONFOUNDING FACTORS

Robert Hooke claimed to have detected stellar parallax around 1660. However, what he actually observed was an equally interesting phenomenon called "stellar aberration", as shown by Bradley in 1720. Basically, this effect results from the fact that a telescope on Earth is moving relative to the Sun frame. Since light travels at a finite speed, this results in an apparent shift of 40 seconds of arc from one side of the Earth's orbit to another (see the diagram below).

The magnitude of the shift can be computed from the ratio of the velocity of the Earth in its orbit to the velocity of light. This ratio is one part in 10,000. Two other confounding factors were observed during the attempts to measure stellar parallax. First, Edmund Halley (of comet fame) observed the "proper motion" of stars in 1718. It turns out that stars are not fixed in space, but are actually moving relative to the Earth. This "proper motion" can be detected for nearby stars. Secondly, Herschel discovered in 1803 that some stars orbit around companions in so-called "binary" systems. This provided the first proof that Newton's gravitational law applied outside the solar system. All of these effects must be properly accounted for in attempts to measure distances via stellar parallax.