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FromTheMoon [43]
3 years ago
6

it is possible for two stars to have different temperatures and different sizes but the same luminosity. explain how.

Geography
1 answer:
Darina [25.2K]3 years ago
6 0

Answer:

Two stars (a and b) can have the same luminosity, but different surface area and temperature if the following condition is met:

(T_a^4)(R_a^2) = (T_b^4)(R_b^2)

Explanation:

The luminosity of a star is the total energy that produces in one second. It depends on the size of the star and its surface temperature.

L = σ(T^4)(4πR^2)

L is the luminosity f the star, T is the temperature of the surface of the star and R is its radius.  

Two stars can have the same luminosity if the relation between the radius and the surface temperature is maintained.  

To see this lets suposed you have 2 stars, a and b, and the luminosities of each one of them:

L_a = σ(T_a^4)(4πR_a^2)

L_b = σ(T_b^4)(4πR_b^2)

you can assume that L_a and L_b are equal:

σ(T_a^4)(4πR_a^2) = σ(T_b^4)(4πR_b^2)

Now, you can cancel the constants:

(T_a^4)(R_a^2) = (T_b^4)(R_b^2)

as long as this relation between a and b is true, then the luminosity can be the same.

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