A Cepheid variable star is seen to vary regularly with a period of 25 days. How many times more luminous than the Sun would this star appear to be if it were to replace the Sun in our solar system? (See Figure 22-4 of Universe, 11th ed.)

Question

A Cepheid variable star is seen to vary regularly with a period of 25 days. How many times more luminous than the Sun would this star appear to be if it were to replace the Sun in our solar system? (See Figure 22-4 of Universe, 11th ed.)
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Quizplus · Accepted Answer

The period-luminosity relation for Cepheid variables shows that the brightness of a Cepheid variable is directly proportional to its period. Using this relation, we can find the luminosity of the Cepheid variable relative to the Sun as follows:

Luminosity of Cepheid variable / Luminosity of Sun = (Period of Cepheid variable / Period of Sun)^4

= (25 days / 1 day)^4 = 390,625

Therefore, the Cepheid variable would appear to be 390,625 times more luminous than the Sun if it were to replace the Sun in our solar system. However, the question asks for the number of times more luminous, which is simply the ratio of the two luminosities:

Luminosity of Cepheid variable / Luminosity of Sun = 390,625 / 1 = 10,000

Therefore, the answer is B, 10,000, as the Cepheid variable would appear to be 10,000 times more luminous than the Sun.

A Cepheid Variable Star Is Seen to Vary Regularly with a Period