# Luminosities and Apparent Brightness of Two Stars of which one is 8 times the distance of the first star [duplicate]

Suppose two stars have the same apparent brightness, but one star is 8 times further away than the other. What is the ratio of their luminosities? Which one is more luminous, the closer or the further star?

## marked as duplicate by Rob Jeffries, Reinstate Monica, peterh says reinstate Monica, Jan Doggen, Mike GFeb 2 at 23:52

• Why don't you do your own homework? The answer is readily resolved using the ideas presented to you in the previous homework question you asked. – Rob Jeffries Feb 2 at 7:47

Since this perceived brightness is something called flux density (sometimes referred to as just flux), which the following formula holds its own for: $$F = \frac{L}{4\pi r^2}$$ ($$L$$ is the luminosity, and $$r$$ is the distance) it would mean the luminosity ratio can be calculated in the following manner:
$$F_A = F_B$$
$$\frac{L_A}{4\pi r_A^2} = \frac{L_B}{4\pi r_B^2}$$
Substituting for $$r_A = 8r_B$$:
$$\frac{L_A}{64r_B^2} = \frac{L_B}{r_B^2}$$
$$L_A = 64L_B$$