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91Ó°ÊÓ

How many times brighter is a star with apparent magnitude 2 than a star with apparent magnitude \(17 ?\)

Short Answer

Expert verified
A star with an apparent magnitude of 2 is \(1,000,000\) times brighter than a star with an apparent magnitude of 17.

Step by step solution

01

Identify the given magnitudes

We have two stars with apparent magnitudes 2 and 17. Our goal is to find the ratio of brightness between these two stars. Star A: Apparent magnitude = 2 Star B: Apparent magnitude = 17
02

Calculate the difference in apparent magnitudes

To find the difference in apparent magnitudes, subtract the magnitude of star A from the magnitude of star B. Difference in magnitudes = Star B magnitude - Star A magnitude = 17 - 2 = 15
03

Use the brightness formula

Now we'll use the formula for relative brightness to find the ratio of brightness between the two stars: Relative brightness = 100 ** (difference in apparent magnitude / 5) Substitute the difference in magnitudes we found in Step 2: Relative brightness = 100 ** (15 / 5)
04

Calculate the relative brightness

Simplify the expression to find the relative brightness: Relative brightness = 100 ** 3 = 1,000,000 So, a star with an apparent magnitude of 2 is 1,000,000 times brighter than a star with an apparent magnitude of 17.

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