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How to Convert Angular Distance to Parsecs

In 1632 Galileo was tried and found "vehemently suspect of heresy" for daring to suggest that the Earth was not the center of the universe and that the stars were not equidistant from us. Today we know that there millions of stars, and that they are all different distances from Earth. When the distances to two stars are known and the angular distance between them is also known, the distance between the stars can be calculated in units called "parsecs." A parsec is 3.26 light-years or nineteen trillion miles.

Things You'll Need

Scientific calculator

Instructions

- 1
  Use the cosine rule to derive the distance between two stars by substituting into the formula the angular distance and the distance from Earth to each of the stars. The cosine rules states that a^2 = b^2 + c^2 - 2bc cosA, where "a" is the unknown distance between the stars, "b" and "c" are the distances to the stars and "A" is the angular distance. For example, if the angular distance is 20 degrees and the stars are known to be 30 and 40 parsecs away the formula becomes a^2 = 30^2 + 40^2 - 2 x 30 x40 cos 20.
- 2
  Reduce the equation to a more simple form by calculating each of the individual components. For example, the original equation becomes (a^2 = 900 + 1,600 - 2,400 cos A), and this can be reduced further to a^2 = 2,500 - 2,400 x cos A
- 3
  Determine the cosine of the angular distance, and then substitute it into the equation. For example, the cosine of 20 degrees is 0.9397, so the equation becomes a^2 = 2,500 - 2,400 x 0.9397, or a^2 = 244.74.
- 4
  Calculate the square root of the A^2 value. The result is the distance between the stars, measured in parsecs. For example, the square root of 244.74 is 15.64, so the distance between the stars is 15.64 parsecs.

Astronomy