Understanding the Magnitude System
The magnitude system is a logarithmic scale. This means that a difference of 1 magnitude corresponds to a specific brightness ratio, not a linear difference.
* A difference of 5 magnitudes equals a brightness ratio of 100.
Calculating the Brightness Difference
1. Find the magnitude difference: 7 - 4 = 3 magnitudes
2. Determine the brightness ratio: Since 5 magnitudes correspond to a brightness ratio of 100, we need to figure out the ratio for 3 magnitudes. We can use the following formula:
* Brightness Ratio = 100^(Magnitude Difference / 5)
* Brightness Ratio = 100^(3/5)
* Brightness Ratio ≈ 15.85
Conclusion
A magnitude 4 star is approximately 15.85 times brighter than a magnitude 7 star.
