Question

In: Physics

11b - Estimating Stars types How would you go about estimating the size of the star...

11b - Estimating Stars types

How would you go about estimating the size of the star called Betelgeuse using its absolute magnitude (-6) and its spectral class (M)? How many Sun's would it take to cross the diameter of Betelgeuse? The volume of Betelgeuse compared to the Sun. What about Rigel, a Blue Giant star? How does it compare to the Sun?

Expert Solution

According to the question, the spectral type of the star Betelgeuse is M and its absolute magnitude is -6.

The spectral type M correspond to the surface temperature of 3000 K.

The relationship between absolute magnitude and luminosity is given by

where L_* is the luminosity of a zero magnitude star (Vega).

Here the luminosity of Vega is 40.12 .

Again we know that,

Where L is luminosity, R is radius, T is absolute temperature.

Thus,

$=> \left ( R/{R_{\bigodot }} \right )^{2} = \left ( L/L_{\bigodot }\right ) \times \left ( T_{\bigodot } /T )^{4 }= 10077.688\times \left (5800/3000 \right )^{4} = 10077.688\times 13.971 = 140795.38$

Thus, it would take approximately 751 Suns to cross Betelgeuse's Diameter.

Since , the volume of Betelgeuse will be times of the sun.

In case of a blue giant star, the radius is 5-10 times that of the Sun and the surface temperature is around 10000 K.

The estimated radius and Surface temperature of Rigel is 75 and 2

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