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→Measuring stellar magnitudes
The visual magnitude system is defined as follows: a star of any given magnitude is about 2.512 times as bright as is a star of the next magnitude. [[Hipparchus]] devised the magnitude system, and [[Ptolemy]] refined it further. By convention, an arbitrary sample of the twenty brightest stars that they could observe were assigned to the first magnitude, and the stars that they could barely observe were assigned to the sixth. Sixth-magnitude stars are actually 100 times less bright than first-magnitude stars. Magnitude levels between these extremes are assigned on a logarithmic scale. Thus, given two stars of brightness l<sub>1</sub> and l<sub>2</sub>, their magnitude difference (V<sub>2</sub> - V<sub>1</sub>) relates to their respective brightnesses in this way:<ref name=Haworth>Haworth, David. "[http://www.stargazing.net/david/constel/magnitude.html Star Magnitudes]." ''[http://www.stargazing.net/david/index.html Observational Astronomy]'', 2003. Accessed January 24, 2019.</ref>
The visual magnitude system is defined as follows: a star of any given magnitude is about 2.512 times as bright as is a star of the next magnitude. [[Hipparchus]] devised the magnitude system, and [[Ptolemy]] refined it further. By convention, an arbitrary sample of the twenty brightest stars that they could observe were assigned to the first magnitude, and the stars that they could barely observe were assigned to the sixth. Sixth-magnitude stars are actually 100 times less bright than first-magnitude stars. Magnitude levels between these extremes are assigned on a logarithmic scale. Thus, given two stars of brightness l<sub>1</sub> and l<sub>2</sub>, their magnitude difference (V<sub>2</sub> - V<sub>1</sub>) relates to their respective brightnesses in this way:<ref name=Haworth>Haworth, David. "[http://www.stargazing.net/david/constel/magnitude.html Star Magnitudes]." ''[http://www.stargazing.net/david/index.html Observational Astronomy]'', 2003. Accessed January 24, 2019.</ref>
<math>\,\!V_2 - V_1 = 2.5 \times \log \frac{l_1}{l_2}</math>
:<math>V_2 - V_1 = 2.5 \times \log \frac{l_1}{l_2}</math>
The ''absolute'' magnitude of any star is the visual magnitude that it would have if it were ten parsecs distant. To convert apparent magnitude V to actual magnitude M, use this formula:
The ''absolute'' magnitude of any star is the visual magnitude that it would have if it were ten parsecs distant. To convert apparent magnitude V to actual magnitude M, use this formula:
<math>\,\!M = V + 5 \times \log \frac{s_0}{s}</math>
:<math>M = V + 5 \times \log \frac{s_0}{s}</math>
where s<sub>0</sub> is the standard distance. This distance is ten [[parsec]]s, or about 2,062,650 AU.
where s<sub>0</sub> is the standard distance. This distance is ten [[parsec]]s, or about 2,062,650 AU.
Brightness declines with the square of distance, and squares correspond to doubling of logarithms. One must then multiply that result by 2.5 to stay within the magnitude scale.
Brightness declines with the square of distance, and squares correspond to doubling of [[logarithm]]s. One must then multiply that result by 2.5 to stay within the magnitude scale.
== Stellar colors and spectra ==
== Stellar colors and spectra ==