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A star or other astronomical body's distance modulus (μ) is an indication of its distance consisting of the difference between its apparent magnitude and its absolute magnitude. It is directly related to the distance to the star if there is no intervening absorption and/or scattering (reddening).
μ = 5 log10d - 5
An object's luminosity distance (dL) is the distance implied by the distance modulus, i.e., a distance to the object implied by the object's actual absolute magnitude and its apparent magnitude. The term luminosity distance is basically just the actual distance for distances to Milky Way stars if reddening is not a big issue, but for objects at cosmological distances (high redshift), curvature can make the actual distance diverge from that implied by the above relation. Straightforward determination of this luminosity distance using the above equation is possible if the actual absolute magnitude is known by some other means, such as if it is a standard candle.