Understanding the Magnitude System

The magnitude system is logarithmic, meaning that a difference of 1 magnitude corresponds to a specific brightness ratio. Specifically:

* A difference of 1 magnitude means one star is 2.512 times brighter than the other.

The Calculation

1. Brightness Ratio: You've stated that one star is 40 times brighter than the other.

2. Logarithmic Calculation: We need to find the power of 2.512 that equals 40. This is done using logarithms:

* log(2.512) * x = log(40)

* x = log(40) / log(2.512)

* x ≈ 3.98

3. Magnitude Difference: The difference in magnitudes is approximately 3.98. Since magnitudes are usually expressed as whole numbers or fractions, we can round this to approximately 4 magnitudes.

Conclusion

The star that is 40 times more intense than the other would be approximately 4 magnitudes brighter.