Question

Calculate the ratio of temp of stars1 wih absolute magnitude_3and radius_72and star 2 with magnitude 8and radius 6

Answer 1

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

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

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