* The Magnitude Scale: The magnitude scale is logarithmic, meaning each step represents a significant change in brightness. A smaller magnitude number indicates a brighter star.
* The Difference: A difference of one magnitude corresponds to a brightness ratio of about 2.512.
* Calculating the Difference: Since we have a 4 magnitude difference (5 - 1 = 4), we need to raise 2.512 to the power of 4.
* Result: 2.512 ^ 4 ≈ 39.8
Therefore, a first magnitude star is approximately 39.8 times brighter than a fifth magnitude star.
