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1 February, 08:07

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

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  1. 1 February, 11:12
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    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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