How did we start accurately measuring the distance and size of astral bodies?
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Measuring the size of a star from arbitrary distances away is pretty easy. Stars change color depending on their size, with brown dwarfs barely emitting enough light to even be detected, to yellow midsize stars like our own, to red giants which explode in a short 100,000 years. So we can tell how large a star is by looking at its colors.
But wait! Don’t objects extremely far from us start accelerating away, and doesn’t this redshift their light the same way a siren gets lower pitched as it moves away from you? How, then would we know what the colors actually are? Answer: Emission spectra. Stars emit all frequencies of light to some degree, but they will also emit specific bands of light corresponding to specific elements. These banding patterns are always the same for those elements no matter the size of the star. So we can analyze the light coming off the distant star, find those bands, and figure out how much the light was redshifted by looking at how much those emission spectrum lines were shifted off what they should be. Shift all the light coming from the star by the same amount, and you have the color of the star.
Redshift also helps with distance. For extremely distant objects, the ordinary, Newtonian motion of the object relative to Earth is irrelevant in comparison to the speed of the expansion of space, so you can model all of those objects as stationary other than the redshift. Since redshift varies more or less constantly with distance, knowing the redshift on an object also gives you an estimate of how far away it is.
For objects within our galaxy, there is no redshift. However, there are a few more tricks we can pull. The easiest is parallax. Take a picture of the sky at one point in Earth’s rotation, wait 6 months, and take another. This will act like our eyes do to give us depth perception, as the objects will be in slightly different positions in the two pictures depending on how far away they are. This also helped us get benchmarks on how large stars were initially. Once you know how far away something is, you can use the intensity of light it emits, and a bunch of math related to stellar fusion, to figure out how bright and large it would be “in person.”
There are many other methods, those are just the easiest to explain.
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