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## Measuring the Distance to Stars

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**The Parallax Method**• To the naked eye stars are so far away that they do not appear to change positions even though we are rotating (8,000 miles wide) and revolving (186, 000,000 miles). • However with the invention of photography, we had new tool to record stars and look for tiny shifts in their position**The Parallax Method**• The first time we were able to see a tiny shift in the position of a star was in 1916 during the First World War. • The shifts are less than an arcminute and were only possible because of the improvements of photography and telescopes.**The Parallax Method**• We use the orbit of the Earth to make our measurements. • By taking pictures 6 months apart we have moved about 186,000,000 miles. • This change of position makes the nearby stars appear to shift compared to the more distant stars. • By recording the angle of the shift we can calculate the distance to the star.**The Parallax Method**• For very small angles we can assume that the sine of the angle is very close to the value of the angle itself (using radians as the measure). • Therefore: Sin θ = opp/hyp and • Hyp = opp/sin θ or Hyp = opp/ θ**The Parallax Method**• However, to simplify things astronomer have developed an easier formula based on the parsec. • 1 parsec = 3.26 light year, where • 1 light year = 5.88 trillion miles • The formula is d = 1/p where d is distance in parsecs and p is the parallax measured in arc seconds.