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Question 44.3: Apparent brightness. Suppose a particular star has intrinsic......

Apparent brightness. Suppose a particular star has intrinsic luminosity equal to that of our Sun, but is 10 ly away from Earth. By what factor will it appear dimmer than the Sun?

APPROACH The luminosity L is the same for both stars, so the apparent brightness depends only on their relative distances. We use the inverse square law as stated in Eq. 44-1 to determine the relative brightness.

b=\frac{L}{4 \pi d^{2}}. (44-1)

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Using the inverse square law, the star appears dimmer by a factor

\frac{b_{\text {star }}}{b_{\text {Sun }}}=\frac{d_{\text {Sun }}^{2}}{d_{\text {star }}^{2}}=\frac{\left(1.5 \times 10^{8} \mathrm{~km}\right)^{2}}{(10 \,\mathrm{ly})^{2}\left(10^{13} \mathrm{~km} / \mathrm{ly}\right)^{2}} \approx 2 \times 10^{-12}

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