A star with a radius three times that of the Sun and a surface temperature twice that of the Sun, will have a luminosity _______ times as great as the Sun's luminosity.

Answer 1

The luminosity of a star follows the equation L = Area X flux = 4π R² × σ_SB T⁴

Since the question is comparing the star to the Sun, this equation can be rewritten by taking the ratio of the luminosity of the star divided by the luminosity of the Sun, reducing and cross-multiplying to get:

L = L_Sun × (a)² × (b)⁴, where a is the ratio of the radius of the star to the radius of the Sun (R_star/R_Sun), and b is the ratio of the temperature of the star to the temperature of the Sun (T_star/T_Sun),

L = (3)² × (2)⁴ × L_Sun = 72 L_Sun