By Suzanne S. Wiley • Updated Mar 24, 2022
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When we observe a star from Earth, the slight shift in its apparent position—called stellar parallax—depends on our planet’s orbit. Parallax is measured as the angle subtended by the Earth’s position now, the star, and the Earth’s position three months earlier or later. Because these angles are tiny, we express them in arcseconds (1/3600 of a degree). The distance to the star, expressed in parsecs, is derived from the reciprocal of its parallax in arcseconds.
Distance (parsecs) = 1 ÷ parallax (arcseconds). If the parallax is given in milliarcseconds, first divide by 1 000, then take the reciprocal.
Some of the farthest stars have parallax values written in milliarcseconds. To convert, simply divide by 1 000. For example, 3 mas = 0.003″.
Take the reciprocal of the parallax in arcseconds. For instance, Proxima Centauri’s parallax is 0.77″, yielding a distance of 1 ÷ 0.77 ≈ 1.30 parsecs. The farther a star, the smaller its parallax and the larger the resulting parsec value.
With the distance in hand, you can relate apparent and absolute magnitudes using the formula:
m – M = –5 + 5 × log₁₀(d), where d is distance in parsecs.
Use the LOG key on your calculator to compute the logarithm.
