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How to Determine a Star's Distance Using Parallax

To correctly interpret the light coming from distant stars, scientists must know how far away a star is. That can't be measured directly. That's where parallax comes in. Parallax is the apparent motion of two objects as an observer moves. If you're sitting at your kitchen table looking at your coffee cup, you see it right in front of the right edge of a cabinet, perhaps. But if you move your head while looking at your cup, it now appears in front of the left edge of the cabinet. The cup hasn't moved, the cabinet hasn't moved, but your perspective has changed. That's parallax, and it can be applied to measuring the distance to stars.

Things You'll Need

Telescope
Astronomical camera

Instructions

- 1
  Focus your telescope on the star of interest. Take a picture of the scene. Include Star A, the one you're measuring the distance to, and Star B, a much more distant star.
- 2
  Wait six months and focus your telescope on the same region of the sky. Take a picture of the scene. Include both Star A and Star B in the picture.
- 3
  Calculate the angle between Star A and Star B as seen in the first picture. The angle will be the separation between the two stars in the photograph divided by the focal length of the telescope.
  
  For example, you might measure the separation between Star A and Star B as 0.0314 mm. If your telescope has a focal length of 800 mm, then the angle is given by:
  
  separation/focal length = .0314/800 = 3.93 x 10^-5 = 39.3 microradians.
- 4
  Convert the angle to arcseconds. The conversion is arcseconds = microradians/4.85. So the angle is 39.3/4.85 = 8.10 arcseconds.
- 5
  Calculate the same angle for the second picture.
  
  In this picture, for example, you might find a separation of 0.0335 mm, which is an angle of .0335/800 = 41.9 microradians, which is 41.9/4.85 = 8.64 arcseconds.
- 6
  Calculate the difference between the two angles and divide by two. This is the parallax half-angle, and it represents how far the star appears to move when the observer moves a distance equal to one astronomical unit; that is, the radius of the Earth's orbit.
  
  For the example, this is (8.64 - 8.10)/2 = .54/2= .27 arcseconds.
- 7
  Take the inverse of the angle calculated in the previous step. The distance to the star, measured in parsecs, is given by the inverse of the angle in arcseconds.
  
  The star in the example is 1 / .27 arcseconds = 3.70 parsecs. One parsec is 3.26 light years, so you can convert this to light years, if you wish: 3.70 x 3.26 = 12.1 light years.

Astronomy