How much brighter is a magnitude +2 star compared to a magnitude +7 star?

Answer

Approximately 99.5 times brighter.

To determine the brightness difference between stars separated by multiple magnitude steps, the fundamental factor of 2.512 must be compounded for each step involved. Comparing a magnitude +2 star to a magnitude +7 star involves a difference of five full magnitude steps (7 minus 2 equals 5). Therefore, the brightness ratio is calculated by raising the base factor to the power of the step difference: $(2.512)^5$. This calculation yields a result of approximately 99.5. This means that the light reaching an observer from the magnitude +2 star is nearly one hundred times greater than the light received from the magnitude +7 star, illustrating the significant compression the magnitude scale achieves in representing vast differences in observed light energy.

How much brighter is a magnitude +2 star compared to a magnitude +7 star?

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