Answer to Question #105844 in Astronomy | Astrophysics for hitendra

Question #105844
A main sequence star has mass 2×1031 kg and radius 3×109
m. Obtain an estimate of the
average temperature throughout the star. Examine if Newton’s theory would be adequate
for the study of this star.
1
Expert's answer
2020-03-19T11:30:55-0400

For a main sequence star with mass 2×1031 kg and radius 3×109 m the average temperature can be found relative to the Sun according to the following expression:


"\\frac{L_{\\text{star}}}{L_{\\text{Sun}}}=\\bigg(\\frac{r_{\\text{star}}}{r_{\\text{Sun}}}\\bigg)^2\\bigg(\\frac{T_{\\text{star}}}{T_{\\text{Sun}}}\\bigg)^4."


Here we have:

"T_{\\text{Sun}}=5778\\text{ K},\\\\\nr_{\\text{Sun}}=6.96\\cdot10^8\\text{ m},\\\\\nm_{\\text{Sun}}=1.9891\\cdot10^{30}\\text{ kg}."


Find the mass ratio relative to the Sun:


"m=\\frac{m_{\\text{star}}}{m_\\text{{Sun}}}=\\frac{2\\cdot10^{31}}{1.9891\\cdot10^{30}}=10.05."

For such a ratio, since "2<m<20", we have


"\\frac{L_{\\text{star}}}{L_{\\text{Sun}}}=m^{3.5},\\\\\n\\space\\\\\nT_{\\text{star}}=T_{\\text{Sun}}m^{\\frac{3.5}{4}}\\sqrt{\\frac{r_{\\text{Sun}}}{r_{\\text{star}}}}=20961\\text{ K}."

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