The Distance to Alpha Centauri
Let us estimate the distance to the nearby star alpha Centauri using its spectral and
luminosity classes.
It is observed to be a G2V star, like our Sun, with apparent visual magnitude m
= -0.01.
Let us take our Sun as a representative G2V star. The Sun's absolute visual magnitude
is M = 4.82.
Then, if we assume that all G2V stars have the same absolute magnitude, we may use
our preceding formulas to write
d(pc) = 10(m - M + 5) / 5
=10(-0.01 - 4.82 +5) / 5 = 1.08 pc
Precision Hipparcos measurements give a parallax of 0.74212 with only 0.2 percent uncertainty.
The true distance then is d = 1 / 0.74212 = 1.35 pc, and our simple estimate
is too low by about 20 percent (not bad, considering the simplicity of the method). Try an
example yourself. Vega is an A0 main sequence
star with apparent magnitude 0.04. Systematics of
HR diagrams suggest that the absolute magnitude of an A0V star is about 0.7. Applying the
same analysis to Vega as that shown above for alpha Centauri,
you should find a distance to Vega of 7.4 pc,
which is only 5 percent lower than the correct distance of 7.76 pc determined by parallax.
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