Definition of luminosity is the total amount of energy emitted by the star per unit of time. We can use following formula to calculate the luminosity:
[tex]L=A\sigma T^4[/tex]
Where A is the surface area of the star.
We also have a very important mass-luminosity relationship:
[tex]\frac{L}{L_0}=(\frac{M}{M_0})^{3.5}[/tex]
This formula gives us relationship between stars mass and it's luminosity. [tex]L_0,M_0[/tex] stands for Sun's luminosity and mass.
We can rewrite the luminosity formula like this:
[tex]\frac{L}{\pi r^2}=\sigma T^4[/tex]
Now if we divide this by the Sun's luminosity we get:
[tex]\frac{L/L_0}{r^2/r_0^2}=(\frac{T}{T_0})^4\\
\frac{(M/M_0)^{3.5}}{M/M_0}=(\frac{T}{T_0})^4\\
(\frac{M}{M_0})^{2.5}=(\frac{T}{T_0})^4\\[/tex]
We can use this formula to estimate the mass. Surface temperature of the Sun is 5778 K.
[tex](\frac{M}{M_0})^{2.5}=(\frac{9800}{5778})^4\\
(\frac{M}{M_0})^{2.5}=8.275\\
\frac{M}{M_0}=2.328\\
M=2.328M_0[/tex]
The answer would be 2 solar masses.
