Question

Calculate the ratio of the surface temperatures of the stars A and B from the
following data:
Star Absolute magnitude Radius (RQ)
A 2 62
B 6 4

Answer 1

Answer on Question #69694 – Physics – Astronomy | Astrophysics

Calculate the ratio of the surface temperatures of the stars A and B from the following data:

Solution. We have the following formulae for the ratio of star luminosities:

$$\frac {L _ {A}}{L _ {B}} = 1 0 ^ {0. 4 (M _ {B} - M _ {A})},$$

where $M_{A,B}$ are absolute magnitudes of the stars $A$ and $B$ .

Using the Stephan-Boltzmann law $L = 4\pi R^2\sigma T^4$ , we obtain

$$\frac {R _ {A} ^ {2} T _ {A} ^ {4}}{R _ {B} ^ {2} T _ {B} ^ {4}} = 1 0 ^ {0. 4 (M _ {B} - M _ {A})},$$

or

$$\frac {T _ {A}}{T _ {B}} = \left(\frac {R _ {B} ^ {2}}{R _ {A} ^ {2}} 1 0 ^ {0. 4 (M _ {B} - M _ {A})}\right) ^ {\frac {1}{4}} \approx 0. 6 4.$$

Answer: $\frac{T_A}{T_B} \approx 0.64$ .

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