Answer to Question #105280 in Astronomy | Astrophysics for Nitesh

Question #105280
Calculate the ratio of temp of stars1 wih absolute magnitude_3and radius_72and star 2 with magnitude 8and radius 6
1
Expert's answer
2020-03-13T10:56:57-0400

We have

"M_1=3^m"

"R_1=72"

"M_2=8^m"

"R_2=6"

Record the luminosities of each star

"L_1=4\\pi R_1^{2}\\sigma T_1^{4}"

"L_2=4\\pi R_2^{2}\\sigma T_2^{4}"

We apply the Pogson formula

"\\frac{L_2}{L_1}=2.512^{M_1-M_2}"

Substitute luminosities

"\\frac{4\\pi R_2^{2}\\sigma T_2^{4}}{4\\pi R_1^{2}\\sigma T_1^{4}}=2.512^{M_1-M_2}"

Simplify the expression

"\\frac{ R_2^{2} T_2^{4}}{R_1^{2}T_1^{4}}=2.512^{3-8}"

"\\frac{ R_2^{2} T_2^{4}}{R_1^{2}T_1^{4}}=2.512^{-5}=0.01"

Where will we write

"\\frac{ T_2}{T_1}=\\sqrt[4]{0.01 \\cdot \\frac{R_1^{2}}{R_2^{2}}}"

"\\frac{ T_2}{T_1}=\\sqrt[4]{0.01 \\cdot \\frac{72^{2}}{6^{2}}}=\\sqrt[4]{0.01 \\cdot 144}=1.095"


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