A star has apparent magnitude 14 and absolute magnitude 7.5. How far away is it (parsecs)?

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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The apparent magnitude of a star is defined as its brightness at a given distance and is generally denotes by m. Absolute magnitude, M, on the other hand, is the apparent magnitude of a star when it is at a distance of 10 parsecs. We can use the absolute and apparent magnitude to calculate the distance of a star in parsec by using the following relationship:

m - M = 5 log (d/10)

Where, d is distance in parsecs.

Substituting the values of apparent and absolute magnitude into the equation, we get

14 - 7.5 = 5 log (d/10) = 6.5

Or, log(d/10) = 6.5/5 = 1.3

Solving the equation, we get d as 199.5 parsecs, that is, the star is almost 200 parsecs (or about 650 light years) away from us. 

Hope this helps.