Aldebaran in the constellation Taurus and Betelgeuse in the constellation Orion are among the brightest stars?
The apparent magnitude of Aldebaran is m=0.85mag and of Betelgeuse is m=0.42mag . We know that the distances to Aldebaran is about 50.1 milli-arcsec and to Betelgeuse 7.6 milli-arcsec. What are the absolute magnitudes of Aldebaran and Betelgeuse and how do their luminosities compare?
October 1st, 2010 at 8:51 am
Yes.
Please explain what part of your HOMEWORK you have questions about.
October 1st, 2010 at 9:50 am
OK, the *parallax* of Aldebaran is about 50.1 milli-arc seconds. That is *not* its distance. The distance to a star in parsecs is gotten by taking one over the parallax in arc seconds. Thus, Aldebaran’s distance is 1/0.0501 or 20 parsecs (65 light years) away. If Betelgeuse has a parallax of 0.00760 arc seconds (7.6 milli-arc seconds), its distance would be roughly 132 parsecs or 429 light years away.
The absolute magnitude of a star is the magnitude it would appear to have at a distance of 10 parsecs (32.6 light years). To get the absolute magnitude, one uses the distance modulus formula:
m – M = 5*Log(d) – 5, where m is the visual magnitude, M is the absolute magnitude, and d is the distance to the star in parsecs (Log is the base-10 logarithm). If Aldebaran has a visual magnitude of 0.85 and a distance of 20 parsecs, its absolute magnitude would be -0.66. You can calculate the absolute magnitude of Betelgeuse the same way.
As for luminosity, the difference of the absolute magnitudes of two stars is related to the luminosities of the two by the following equation: M2 – M1 = 2.5*Log (L1/L2), where L2 is the luminosity of the 2nd star and L1 is the luminosity of the first star. This should allow you to compare the luminosities of Aldebaran and Betelgeuse.