Question

A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = –2.78(log P) – 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.

Answer 1

-5.95

Explanation:

M = –2.78(log P) – 1.35 where M = absolute magnitude and P = period or length of pulse.

From our question, it is given that P = 45 days.

So, M = –2.78(log P) – 1.35

M = –2.78(log 45) – 1.35

M = –2.78(1.6532) – 1.35

M = -4.60 - 1.35

M = -5.95

So, the absolute magnitude or brightness M of a Cepheid star after a period P of 45 days is -5.95

Answer 2

The absolute brightness of the Cepheid star after a period of 45 days is -5.95

Explanation:

Since the absolute magnitude or brightness of a Cepheid star is related to its period or length of its pulse by

M = –2.78(log P) – 1.35 where M = absolute magnitude and P = period or length of pulse.

From our question, it is given that P = 45 days.

So, M = –2.78(log P) – 1.35

M = –2.78(log 45) – 1.35

M = –2.78(1.6532) – 1.35

M = -4.60 - 1.35

M = -5.95

So, the absolute magnitude or brightness M of a Cepheid star after a period P of 45 days is -5.95