Final answer:
A star with an apparent magnitude of -1 is about 100 times brighter than a star with an apparent magnitude of 4, according to the magnitude scale used in astronomy. None of the provided options (A, B, C, D) exactly match this calculation; option A) 125 times brighter is the closest, but still not accurate.
Step-by-step explanation:
The difference between a star with an apparent magnitude of -1 and a star with an apparent magnitude of 4 is specifically calculated using the magnitude scale for star brightness. Since the astronomical magnitude scale is logarithmic, a 1-magnitude difference corresponds to a brightness factor of 2.512 (the fifth root of 100). When we apply this knowledge, we can calculate the difference as follows:
- Determine the difference in magnitude: 4 - (-1) = 5
- Apply the difference to the brightness factor: 2.5125 (since five magnitudes difference)
- Calculate the value: 2.5125 ≈ 100
Therefore, a star with an apparent magnitude of -1 is approximately 100 times brighter than a star with an apparent magnitude of 4. When we explore the provided options, we find that the closest match to the calculated value is 'A) 125 times brighter', although this is not the exact match to the calculated value using the magnitude difference rule. It seems there may be an error in the provided options, as none of them perfectly align with the calculated value. Understanding the apparent magnitude scale is crucial as it helps us grasp the concept of how luminosity and distance affect the brightness of stars as seen from Earth.