Distance Modulus

The distance modulus connects how bright an object looks from Earth with how intrinsically bright it really is. It works because light spreads out over a sphere as distance increases, so the received flux falls off like 1/d^2; the logarithmic magnitude scale then turns that inverse-square law into a simple linear relation in log(distance). A difference of 5 magnitudes corresponds to a factor of 10 in distance, which is why the formula has the form 5 log10(d) - 5 when d is measured in parsecs.

Use this when you know an object's apparent magnitude and absolute magnitude and want its distance, or when you have a measured distance and need to predict how bright it should appear. It is especially useful for stars, supernovae, galaxies, and other objects whose intrinsic luminosities can be estimated or standardized.

• Using kilometres or light-years in the formula instead of parsecs
• Forgetting that the formula uses a base-10 logarithm, not ln
• Reversing m and M, which changes the sign of the distance modulus