Luminosity distance is a term used in astronomy to describe the distance at which an astronomical body would lie based on its observed luminosity in the absence of any unanticipated attenuation. The luminosity distance does however take into account the fact that the observed luminosity is attenuated by two factors, relativistic redshift and the Doppler shift of emission, each of which contributes a attenuation,

where z is the redshift. The observed flux is therefore given by

where is the proper distance and is the emitted luminosity. Solving for then gives

were a is the expansion parameter and r is the actual distance. Now define

giving the luminosity distance