Answer to Question #202900 in Astronomy | Astrophysics for Prachi

Question

What is meant by the apparent magnitude of a star? How is it related to the brightness of the star? An object A has an apparent magnitude of –5. Another object B has an apparent magnitude of –10. Calculate the ratio of their brightness.

Answer 1

The apparent magnitude means the brightness of the object detected by the observer on the Earth. The apparent magnitude depends not only on the luminosity of the object, but also on the distance from the observer to the object. If E is the brightness of the object, then

$m = -2.5\lg E +\text{const}.$ Here E is proportional to the luminosity and inversely proportional to the square of distance.

According to the Pogson's formula,

$m_A - m_B = -2.5\lg \dfrac{E_A}{E_B}, \\ \dfrac{E_A}{E_B} = 10^{0.4(m_B-m_A)} = 10^{0.4(-10+5)} = 10^{-2} = 0.01.$

So the difference between the magnitudes equal to 5 corresponds the ratio of brightnesses equal to 100.