How do we know how far away a star is?
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For objects that are relatively close astronomers use a method based on parallax. That is done by measuring the viewing angle to the star from a point on Earth, or an orbiting telescope, then waiting a period of time, often 6 months, and measuring it again. The difference in that angle lets them calculate the distance. The bigger the distance of the telescope between the first and second measurements allows us to measure objects that are farther away. 6 months is the time for the Earth to be on the opposite side of the orbit of the sun, and us the farthest away we can get the two points. This method only works for objects about a maximum of 400 light-years away.
For objects even farther away, where parallax angles aren’t measurable, they commonly look at the spectrum of light emitted by the star. From that they can determine about how bright the star really is. By comparing that to how dim it looks from Earth they can get an approximation of the distance.
For very distant objects like far away galaxies they can also use red-shift to get an approximate distance. The farther away something is, the more the light from it is shifted to the red end of the spectrum.
We can now use direct measurements for things very close. Radar, and lasers can be used to measure their distance.
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