Two main-sequence stars, Star X and Star Y

PHYSICS · Multi-part · A Level · Physics · Astrophysics · Astrophysics

Problem

Two main-sequence stars, Star X and Star Y, are observed from Earth. • Star X has a measured luminosity of

3.2\times10^{27}\,\text{W}

and an effective surface temperature of

4.0\times10^{3}\,\text{K}

. • Star Y has a measured luminosity of

3.2\times10^{27}\,\text{W}

(the same as Star X) but an effective surface temperature of

8.0\times10^{3}\,\text{K}

. Assume that each star behaves as an ideal thermal radiator. (a) Determine which star has the larger radius. Provide a clear, step-by-step justification that explicitly relates the measured luminosities to the stellar radii. (b) Quantitatively calculate the ratio

\dfrac{R_Y}{R_X}

of the radii of the two stars. (c) Explain, without additional calculation, how the surface temperature of a star influences its luminosity if its radius remains fixed. Connect your explanation to the physical meaning of luminosity.

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