Sirius AJSFH
<Text-field style="Heading 1" layout="Heading 1">Problem</Text-field> Sirius A (Alpha Canis Majoris) is close enough to Earth for accurate parallax measurement of its distance. This knowledge enables an accurate determination of its luminosity. Calculate its (A) mass, (B) radius, and (C) effective temperature, assuming (correctly) that it is a Main Sequence star with mass near that of the Sun. (Data are from Liebert et al., 2005). Hints: Use the equations and data given below
<Text-field style="Heading 1" layout="Heading 1">Data</Text-field> Distance to Sirius in Parsecs 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 JCIkayMhIiM= Luminosity of Sirius in Units of Solar Luminosity 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 JCIkYSMhIiI=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Useful Equations</Text-field> Mass-Luminosity Equation 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 Mass-Radius Equation 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 Temperature-Luminosity-Radius Equation 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
<Text-field style="Heading 1" layout="Heading 1">Solution</Text-field>
<Text-field style="Heading 2" layout="Heading 2">A)</Text-field> Calculate the mass of Sirius in solar masses. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 NiUkIitxKVJVQyMhIiosJiQiKz5OIVIqXCEjNSEiIiomJCIrIjRzej0jRiUiIiJeI0YuRi5GLiwmRidGKkYrRio= 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 NyMkIitxKVJVQyMhIio= JSFH The estimated mass, 2.24 solar masses, is reasonably close to the accepted figure of 2.02 solar masses.
<Text-field style="Heading 2" layout="Heading 2">B)</Text-field> Calculate the radius of Sirius in units of solar radius. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFElMi4yNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYnLUYvNiRRJjAuNzM4RidGMi8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnL0YzUSdpdGFsaWNGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGPUYy JCIrXGVOOD0hIio= The estimated radius, 1.81 times that of the Sun, is reasonably close to the accepted figure of 1.711. C. Calculate the effective temperature of Sirius in kelvins. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LCQqJiQiK21MKVtrKiEiJyIiIkkiS0c2IkYnRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= The estimated effective temperature at the surface, 9645 K, is reasonably close to the accepted figure of 9940 K.
<Text-field style="Heading 1" layout="Heading 1">References</Text-field> ------------------------------------------------------------------- Liebert, J., Young, P., Arnett, D., Holberg, B. and Williams, K. (2005). The Age and Progenitor Mass of Sirius B. Astrophysical Journal, 630, 1, L69-L72.
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