Question

The chart shows characteristics of stars. Sirius is a blue-white star with a surface temperature of about 9800 K. What is most likely the mass of Sirius? 1.0 solar mass 1.4 solar mass 2.0 solar mass 12 solar mass

Answer 1

The answer would be 2 solar masses.

Answer 2

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:

`L=A\sigma T^4`
Where A is the surface area of the star.
We also have a very important mass-luminosity relationship:

`(L)/(L_0)=((M)/(M_0))^(3.5)`
This formula gives us relationship between stars mass and it's luminosity.
`L_0,M_0` stands for Sun's luminosity and mass.
We can rewrite the luminosity formula like this:

`(L)/(\pi r^2)=\sigma T^4`
Now if we divide this by the Sun's luminosity we get:

`(L/L_0)/(r^2/r_0^2)=((T)/(T_0))^4\\ ((M/M_0)^(3.5))/(M/M_0)=((T)/(T_0))^4\\ ((M)/(M_0))^(2.5)=((T)/(T_0))^4\\`
We can use this formula to estimate the mass. Surface temperature of the Sun is 5778 K.

`((M)/(M_0))^(2.5)=((9800)/(5778))^4\\ ((M)/(M_0))^(2.5)=8.275\\ (M)/(M_0)=2.328\\ M=2.328M_0`
The answer would be 2 solar masses.