A star has an apparent magnitude of 6.5 and an absolute magnitude of - 0.8. What is the distance to the star?

Answer: 288.4 pc

Explanation:

The apparent magnitude and absolute magnitude of star are related as:

m = M + 5 log d - 5

where, m is the apparent magnitude from the Earth and M is the absolute magnitude (The magnitude of star if it is at 10 pc distance away from Earth) of the star. Then, d is the actual distance of star in parsecs (pc).

m = 6.5

M = - 0.8

d = ?

⇒ 6.5 = - 0.8 + 5 log d - 5

⇒ 12.3 = 5 log d

⇒ 2.46 = log d

⇒ d = anti-log (2.46) = 288.4 pc

Hence, the star is 288.4 pc away from Earth.