Question

Approximate apparent magnitudes of celestial object A is -23 and of celestial object B is 0.5. How many times brighter is the celestial object A than celestial object B?

Option 1: 1500 times
Option 2: 10000 times
Option 3: 50000 times
Option 4: 100000 times

Answer 1

Celestial object A is approximately 100,000 times brighter than celestial object B as determined by the astronomical apparent magnitude scale. Using the formula 2.512 raised to the power of the difference in magnitudes (23.5), we find that object A is significantly brighter.

Step-by-step explanation:

To determine how many times brighter celestial object A is than celestial object B, we use the concept of apparent magnitude used in astronomy. A difference of 5 magnitudes corresponds to a brightness ratio of 100:1, according to a precise scale established by astronomers based on historical categorizations by Hipparchus.

Using the formula that each step of 1 magnitude difference corresponds to a brightness difference by a factor of approximately 2.512, we can calculate the brightness ratio between magnitudes -23 and 0.5. The difference in magnitudes is 23.5 steps (0.5 - (-23)):

2.51223.5 ≈ 2.51223 × 2.5120.5 ≈ 1011.5 (since 2.51210 roughly equals 104)

This is approximately 100,000 times as bright, making celestial object A 100,000 times brighter than celestial object B. Therefore, the correct option is Option 4: 100,000 times.