# what is the difference between luminosity distance and distance?

This is a very basic question but I am little confuse the difference between luminosity distance and distance. Can anyone tell me that what is the difference between luminosity distance and distance?

The luminosity distance is the apparent distance of an object based on how bright is it and how bright it appears to be. If you have two stars of equal luminosity, the more distant one will appear dimmer.

For local objects, the intensity of the light will obey an inverse-square law. So, for local objects (stars) the luminosity distance is equal to the actual distance.

But for very distant objects, like quasars or distant supernovae, the curvature and expansion of space-time will also affect luminosity. The luminosity distance is the distance obtained by ignoring these factors and just assuming that the intensity of the light from a distant object obeys the inverse square law.

As an example: a type 1a supernove is observed to have a magnitude 18.7, and is assumed to have an absolute magnitude of -19.3

It's luminosity distance in parsecs is $$10^{(18.7+19.3)/5+1} = 398 \text{Mpc}$$

If it has a redshift of z = 0.086 then its co-moving distance (what you would measure with a ruler) is 398/1.086 = 366 Mpc.

• "how bright is it" would require going there and making a measurement. I think "how bright it is expected to be" might be better.
– uhoh
Aug 30, 2020 at 0:29