Thinking back 15 years ago to Astonomy 101, but I think they measure the parallax, and red/blue shift in its spectrum.
Parallax is the apparent shift in position of an object due to a shift in the position of the observer. If you open and close your eyes one at a time, and see how things appear to move, that is parallax.
measuring the apparent MOA (minutes of angle) shift of a celestial body when observed from two different points (as long as we know the distance beyween them) enables us to calculate the distance to the celestial body.
There’s a bunch more math to account for Earth’s rotation and orbit, and I think spectrometry plays a role as well, but IIRC the parallax is the fundamental mechanic that enables us to judge distance from earth.
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