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Chapter 17: Problem 42

Stars \(A\) and \(B\) are both equally bright as seen from Earth, but \(A\) is \(120 \mathrm{pc}\) away while \(B\) is \(24 \mathrm{pc}\) away. Which star has the greater luminosity? How many times greater is it?

Short Answer

Expert verified
Star A has a greater luminosity which is 25 times greater than that of Star B.

Step by step solution

01

Understanding the problem and the equation

We know that, from the inverse square law, the luminosity \(L\) of a star is directly proportional to the square of its distance \(d\) from the observer, the equation can be written as: \(L \propto d^2\). Here 'pc' denotes 'parsecs', a unit of distance in astronomy.
02

Calculating the luminosity of star A relative to B

Let's assume the luminosity of star A is \(L_A\) and of star B is \(L_B\). The ratio of luminosity of A to B can be described as the ratio of squares of their distances: \(\frac{L_A}{L_B} = \frac{d_A^2}{d_B^2}\)
03

Inputting the given values into the equation

By substituting the distance of star A \(d_A = 120pc\) and the distance of star B \(d_B = 24pc\) in the equation we get: \(\frac{L_A}{L_B} = \frac{(120)^2}{(24)^2}\)
04

Solving the equation

Solving the equation, we get \(\frac{L_A}{L_B} = 25\). This means the luminosity of star A is 25 times greater than that of star B.

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