In most disciplines, finding the distance from one object to the next is, at least in theory, a simple operation. Not so in astronomy. While the size of Earth itself was determined with a fair degree of accuracy in ancient times, the scale of the solar system wasn’t fully understood until just a few centuries ago, and the distances to even the closest of stars wasn’t reliably determined until Friedrich Bessel measured the distance to 61 Cygni in 1838.
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Earth’s orbit is slightly elliptical, so astronomers make appropriate adjustments when applying the parallax method for real.
There are some interesting historical reasons for the choice of 360 that lie beyond the scope of this article. A quick hint is to compare this to the number of days in a year.
Tycho, the best observer before the invention of the telescope, cited angular measurements to a precision of 2 arcminutes.
Always excepting the Sun, of course!
And now you know the origin of the biggest astronomical gaffe in cinematic history. Han Solo should be ashamed of himself.