Question

a cepheid star is a type of variable star, which means that 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. use a calculator to solve each problem. round your answers to the nearest hundredth. what is the absolute magnitude of a star that has a period of 62 days? what is the absolute magnitude of a star that has a period of 50 days?

Explanation:

Step1: Substitute \(P = 50\) into the formula

We have the formula \(M=-2.78(\log P)-1.35\). Substituting \(P = 50\) gives \(M=-2.78(\log(50))-1.35\).
We know that \(\log(50)=\log(5\times10)=\log(5)+\log(10)\approx0.69897 + 1=1.69897\) (using a calculator for \(\log(5)\approx0.69897\) and \(\log(10) = 1\)).

Step2: Calculate the value of \(M\)

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Rounding \(-6.07313\) to the nearest hundredth gives \(M\approx - 6.07\)

Answer:

\(-6.07\)