They can be determined with a variety of 'distance indicators' based on a series of empirically derived measurement principles ( parallax, Cepheid light curves, spectral class). This is empirical knowledge based on direct observation, and only very weakly on some 'theory'. Of course everything we do is based on some 'theory' about what to expect. The distance information we have isn't 'just' theoretical however. I would say it is the most fundamental and heavily verified element of astronomical knowledge we work with upon which EVERYTHING else in astronomy hinges to set the scale of the rest of the universe.
The most basic distance measure, used for thousands of years by surveyors on Earth, is the parallax. It measured the minute geometric shifts in the sky positions of over 100,000 stars. This is the most direct way imaginable to get distances, and is the same technique you use with your own pair of eyes to determine how far a book, house or mountain is from you. It is almost 'theory free'. As seen from opposite sides of the Sun 6 months apart, stars shift their sky positions relative to background stars. A star that is 3.26 light years distant ( 1 parsec) shifts 1 second of arc; a star twice this distance shifts 0.5 arcseconds. Alpha Centauri shifts about 0.75 arcseconds so its geometric distance is 4.3 light years.
The Hipparcos satellite re-measured the parallaxes of over 120,000 reference stars an a million others. It's conclusion was that the previous distances used to key Cepheid stars was about 10 percent too small based on the new parallax measurements of these stars. It is satisfying that this ultra precision study resulted in only a 10 percent change in the distances to all objects farther than about 300 light years!
Copyright 1997 Dr. Sten Odenwald
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