It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed entirely implausible: it was one of Tycho Brahe's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere (the fixed stars).
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The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.
Parallax | The Parallax View | Stellar classification | Parallax (comics) | Stellar Kart | Summer's Stellar Gaze | Stellar collision | Stellar wind (code name) | Stellar Wind | stellar wind | Stellar's Sea Eagle | Stellar Classification | stellar classification | Stellar atmosphere | Parallax (Greg Howe album) | parallax | Hypercompact stellar system |