Question

You have discovered a new star in the Milky Way: Your new star is red and has 3/5 the tempera-

ture of our Sun. The new star emits a total power that is 100,000 times greater than the power

emitted by our Sun.

(a) Determine the spectral type (i.e. spectral classification) of the new star.

(b) How many times bigger is the radius of the new star compared to the radius of our Sun?​

Answer 1

Answer:

spectral type M.

878.41 times Radius of stat

Explanation:

Given in the question that,

new star has 3/5 the temperature of sun

(a)

We know that temperature of sun = 5778K

To determine the spectral class of the star we need to know its temperature.

T(new star) = 3/5T(sun)

                   = 3/5(5778K)

                   = 3466.8K

As the temperature of this star is below 3500K and its colour is red, then it belongs to the spectral type M.

(b)

We will use Stefan-Boltzmann formula to calculate the size of radius of new star

Given in the question that, new star emits a total power that is 100,000 times greater than the power.

so,

$\frac{4\pi Rs^2\alpha T^4}{4\pi Rn^2\alpha T^4}=100000$

$\frac{4\pi Rs^2\alpha (\frac{3}{5} T)^4}{4\pi Rn^2\alpha T^4}=100000$

$\frac{81Rs^2\alpha (T)^4}{625Rn^2\alpha T^4}=100000$

Solve for Rn

Radius is approximately 878.41 times bigger than the radius of the Sun.