Distance modulus

Remarks

If no light is absorbed on the way, the definition of $M$ gives $$\mu = 5 \log_{10} \frac{d}{10\ \mathrm{pc}}, \qquad d = 10^{\mu/5 + 1}\ \mathrm{pc}.$$ With interstellar extinction $A$ in magnitudes, $m - M = 5\log_{10}(d / 10\ \mathrm{pc}) + A$. Example: the Large Magellanic Cloud has $\mu \approx 18.5$, so $d \approx 10^{4.7}$ pc $\approx 50$ kpc. Non-example: the difference of the apparent magnitudes of two stars is not a distance modulus; it compares two objects, not one object with itself at $10$ pc. The symbol $\mu$ is the usual notation, though it also denotes proper motion.