What crucial astronomical measurement, successfully achieved by Friedrich Bessel in 1838, proved stars were comparable objects to the Sun?

Answer

Stellar parallax.

The successful measurement of stellar parallax, which demonstrates a star has a finite, measurable distance due to Earth's orbit, provided definitive proof that stars were physical objects comparable to the Sun rather than infinitely distant entities.

What crucial astronomical measurement, successfully achieved by Friedrich Bessel in 1838, proved stars were comparable objects to the Sun?
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