Answer to Question #88567 in Astronomy | Astrophysics for Navdha

Question #88567
Explain what you understand 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
1
Expert's answer
2019-04-26T11:27:35-0400

Apparent magnitude of a star is a measure of its brightness in logarithmic units. By conventional definition, apparent magnitude mm is related to the observed flux density F of light from the star (which is its brightness) by the formula

m=5log100FF0=2.5log10FF0,m = - 5 \log_{100} \frac{F}{F_0} = - 2.5 \log_{10} \frac{F}{F_0} \, ,

where F0F_0 is the reference flux density corresponding to zero apparent magnitude. Since the flux density (brightness) for a star can be measured in different spectral bands (ultraviolet, visible, infrared etc.), one can speak of the apparent magnitude in the corresponding spectral band. For two objects A and B with apparent magnitudes mAm_A and mBm_B, respectively, we have

mAmB=5log100FAF0+5log100FBF0=5log100FBFA.m_A - m_B = - 5 \log_{100} \frac{F_A}{F_0} + 5 \log_{100} \frac{F_B}{F_0} = 5 \log_{100} \frac{F_B}{F_A} \, .

Thus, for mA=5m_A = - 5 and mB=10m_B = - 10, we obtain 5log100(FB/FA)=55 \log_{100} \left( F_B / F_A \right) = 5, or log100(FB/FA)=1\log_{100} \left( F_B / F_A \right) = 1. Hence, the ratio of their brightness is FB/FA=100F_B / F_A = 100


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