astronomy college level

Question

What is the brightness ratio, and associated magnitude change for Deneb at 10 pc?

1/802 and 2.5

1/80.2^2 and 9.57

1/6432 and 2.5

1/802 and 9.57

Answer 1

Distance of Deneb star from the Earth 802 pc

Find brightness ratio use formula apparent brightness

b = L/(4πd^2), L - luminosity and d - distance in meters.

Brightness ratio B_Earth/B₁₀ = [10/802]^2 = 1/(80.2)^2

For magnitude change use distance modulus equation (log at base 10)

Apparent magnitude - Absolute magnitude (magnitude star at 10 pc)

m - M = 5 log d - 5 = 5 log 802 - 5 = 9.52 ≅ 9.57 because distance 802 parsec

is approximate. Therefore, second answer is the correct answer

Ratio 1/(80.2)^2 and magnitude difference 9.57

I hope this helps.

Shailesh (Sky) Kadakia, Expert Astronomy tutor

WYZANT, Inc.