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I was just watching a lecture from Carl Sagan. He talked about figuring out the distance to the stars; it got me interested in learning more about the subject.

As far as I know, the Inverse square law and parallax can be used. Can anyone expand on these? Specifically with regards to what I could do to measure the distance from Earth to Proxima Centauri.

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In order for you to use the inverse square law you must know the distance first (unless you use what's known as a standard candle). –  astromax Nov 13 '13 at 12:56
    
For Proxima Centauri, just use parallax. Record the position of Proxima Centauri (against the "fixed" stars further away from it) 6 months apart, and use the angular distance and the diameter of the Earth's orbit (about 186 million miles) to find the distance. –  barrycarter Nov 17 '13 at 7:01
    
As I have outlined in the comments below, the accepted answer here is barely relevant to standard techniques of determining distance to stars in astronomy. Relevant info can be found instead, e.g. in this reference: en.wikipedia.org/wiki/Spectroscopic_parallax –  Alexey Bobrick Nov 21 '13 at 14:23

2 Answers 2

up vote 3 down vote accepted

One way to find distance to a collection of stars is to hope for an RRLyrae in the bunch. Since RRLyrae are standard candles, you can use the inverse square law to extract the distance.

rrlyraePeriod

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What do you do if there is no RRLyrae? –  FunctionR Nov 13 '13 at 20:08
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What do you do when you don't have RRLyrae and you're beyond the distance parallax can be used? Hope for some other type of variable star or supernovae in order to use as a standard candle, I'd say. Beyond that I'm not entirely sure. Anything too local will not be expanding with the universe in a predictable enough way in order to relate its redshift to distance. All stars we hope to see are unfortunately local (in our own Milky Way galaxy; save for supernovae). –  astromax Nov 13 '13 at 21:17
    
That was very informative. Thank you. –  FunctionR Nov 13 '13 at 22:01
    
This is definitely not a typical method of measuring distances to stars. RR lyrae are red giants and are extremely rare comparing to main sequence stars. What one normally does instead is estimating the absolute magnitude and extinction towards the star, which are in their turn determined by the means of multi-band photometry or spectroscopy. This way one knows the luminosity of the star and hence can derive the distance. In a sense, a star "becomes" a standard candle, once its spectrum is studied (even if by means of photometry). –  Alexey Bobrick Nov 20 '13 at 21:27
    
Hmm - not sure why a correct answer was down-voted. You could have simply said that there are more common techniques. What would have been even better is to come up with an answer of your own. –  astromax Nov 21 '13 at 3:49

For close objects, the parallax method works perfectly. Though for higher distances, the Standard candles, as mentioned before, are used. The brightness of RR Lyrae, Supernovae type Ia, could be calculated, therefore, with the amount of light we get from these objects, we can estimate the distance. For even farther objects, the redshift method is used to calculate the distance, where a given line transition with a given frequency (iron emission for instance) is measured, and the shift in frequency, caused by the expansion of the universe (a phenomenon described mathematically) gives us a hint for the distance of the object.

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