Can the distance to a star be measured?

That time, that place

For nearly three hundred years after Copernicus, no direct evidence showed the Earth moving.

The surest evidence would be annual parallax: if the Earth circles the sun, then half a year later it stands on the far side of its orbit, and a nearby star should appear to shift slightly against the distant background.

Tycho Brahe spent a lifetime of precise observation looking for it and never found it. So he did not accept the moving Earth. His logic was sound: if no parallax shows, then either the Earth does not move, or the stars are unimaginably far.

Why this question

Bessel bet on the stars being unimaginably far. Then the parallax would be tiny, and catching it would need unprecedented precision.

Even choosing the star was a problem. A bright star is not necessarily a near one — brightness mixes distance with the star's own output.

Bessel used a different criterion: a star that moves quickly against the background is probably close. 61 Cygni had the largest known proper motion — a dim, unremarkable star.

At the Königsberg observatory he spent more than a year repeatedly measuring the angle between it and the background stars beside it, with a new instrument.

What was found

The parallax was 0.314 arcseconds — roughly the angle a coin makes from a dozen or so kilometres away.

Converted to distance: about ten light years. The modern figure is a little over eleven, so he was close. Until then nobody knew the distance to any star. Here was the first ruler for anything beyond the solar system.

And after 295 years, direct evidence that the Earth moves. Tycho's objection closed here. He had not been wrong — the stars really were unimaginably far.

That same year Henderson and Struve obtained parallaxes for other stars. Three people arrived almost together. What nobody had managed for three centuries happened in three places at once, as soon as instruments reached the necessary precision.