Question

4. Two stars are imaged by the same telescope/CCD system. If both stars are known to be at the same distance from the Earth and the measured flux arriving at Earth from star B is 10x that from star A... A)What is the magnitude difference between these two stars? (ie., we want Am- m-m) B)Letting LJ be the luminosity of star A and Lg be that of star B, whet is the ratio of their luminosities: .A

Answer 1

a) The relationship is given as

m_B - m_A = -2.5 log (f₁ / f₂)

m_B - m_A = -2.5 log (10)

m_B - m_A = -2.5

m_B - m_A = 2.5

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b) we know

flux = luminosity * distance²

for star A and B

flux (A) / flux (B) = luminosity (A) * distance² (A) / luminosity (B) * distance² (B)

As distance of both stars is same, we have

flux (A) / flux (B) = luminosity (A) / luminosity (B)

Therefore,

L_A / L_B = flux_A / flux_B

L_A / L_B = 1/10

L_A / L_B = 0.1