The stellar magnitude scale is defined such that if two stars differ in brightness by a factor of 100, they differ in magnitude by what magnitudes?
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Savannah 3rd grade Mrs.Love
A factor of 10 is one order of magnitude. So 100 would be 2 orders of magnitude.
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To understand how the stellar magnitude scale works, we need to know that it is a logarithmic scale. It means that the difference in magnitude between two stars is not a simple arithmetic difference, but rather a logarithmic one.
In the case of the stellar magnitude scale, if two stars differ in brightness by a factor of 100, they differ in magnitude by 5 magnitudes. This means that the fainter star would have a magnitude that is 5 units higher than the brighter star.
Now, let's break down how we arrive at this answer:
First, we know that a factor of 10 is one order of magnitude. This means that if two stars differ in brightness by a factor of 10, they differ in magnitude by 1 magnitude. So if we have a ratio of brightness of 10, we have a magnitude difference of 1.
In this case, we have a ratio of brightness of 100. Since 100 is 10 raised to the power of 2 (10^2), we can say that the ratio of brightness of 100 is equivalent to having a magnitude difference of 2 magnitudes.
Therefore, if two stars differ in brightness by a factor of 100, they differ in magnitude by 2 magnitudes.