How to Measure the Distance to the Stars

How to Measure the Distance to the Stars

The separation of the planets from one another – forty million kilometers from Earth to Venus at closes approach, six billion kilometers to Pluto – would have stunned those Greeks who were outraged by the contention that the Sun might be as large as the Peloponnesus.

It was natural to think of the solar system as much more compact and local. If I had my finger before my eyes and examine it first with my left and then with my right eye, it seems to move against the distant background. The closer my finger is, the more it seems to move. I can estimate the distances to my finger from the amount of this apparent motion, or parallax. If my eyes were farther apart, my finger would seem to move substantially more.

The longer the baseline from which we make our two observations, the greater the parallax and the better we can measure the distances to remote objects. Bu we live on a moving platform, the Earth, which every six months has progressed from one end of its orbit to the other, a distance of 300, 000, 000 kilometers.

How far would we have to travel from the Sun for it appear as small and as dim as a star? Illustration by Elena

If we look at the same unmoving celestial object six months apart, we should be able to measure very great distances. Aristarchus suspected the stars to be distant suns. He placed the Sun among the fixes stars. The absence of detectable stellar parallax as the Earth moved suggested that the stars were much farther away than the Sun. Before the invention of the telescope, the parallax of even the nearest stars was too small to detect. Not until the nineteenth century was the parallax of a star first measured. It then became clear, from straightforward Greek geometry, that the stars were light-years away.

There is another way to measure the distance to the stars which the Ionians were fully capable of discovering, although, so far as we know, they did not employ it. Everyone knows that the farther away an object is, the smaller it seems. This inverse proportionality between apparent size and distance is the basis of perspective in art and photography. So the farther away we are from the Sun, the smaller and dimmer it appears. How far would we have to be from the Sun for to appear as small and as dim as a star? Or, equivalently, how small a piece of the Sun would be as bright as a star?

An early experiment to answer this question was performed by Christian Huygens, very much in the Ionian tradition. He drilled small holes in a brass plate, held the plate up to the Sun and asked himself which hole seemed as bright as he remembered the bright star Sirius to have been the night before. The hole was effectively 1/28,000 the apparent size of the Sun (Huygens actually used a glass bead to reduce the amount of light passed by the hole). So Sirius, he reasoned, must be 28,000 times farther from us than the Sun, or about half a light-year away. It is hard to remember just how bright a star is many hours after you look at it, but Huygens remembered very well. If he had known that Sirius was intrinsically brighter than the Sun, he would have come up with almost exactly the right answer: Sirius is 8,8 light-years away. The fact that Aristarchus and Huygens used imprecise data and derived imperfect answers hardly matters. They explained their methods so clearly that, when better observations were available, more accurate answers could be derived.