can be written as where it is assumed that extinction from gas and dust is negligible. Typical extinction rates within the Milky Way galaxy are 1 to 2 magnitudes per kiloparsec, when dark clouds are taken into account. For objects at very large distances (outside the Milky Way) the luminosity distance (distance defined using luminosity measurements) must be used instead of , because the Euclidean approximation is invalid for distant objects. Instead, general relativity must be taken into account. Moreover, the cosmological redshift complicates the relationship between absolute and apparent magnitude, because the radiation observed was shifted into the red range of the spectrum. To compare the magnitudes of very distant objects with those of local objects, a K correction might have to be applied to the magnitudes of the distant objects. The absolute magnitude can also be written in terms of the apparent magnitude and stellar parallax : or using apparent magnitude and distance modulus : Examples Rigel has a visual magnitude of 0.12 and distance of about 860 light-years: Vega has a parallax of 0.129″, and an apparent magnitude of 0.03: The Black Eye Galaxy has a visual magnitude of 9.36 and a distance modulus of 31.06: Bolometric magnitude The bolometric absolute magnitude , takes into account electromagnetic radiation at all wavelengths. It includes those unobserved due to instrumental passband, the Earth's atmospheric absorption, and extinction by interstellar dust. It is defined based on the luminosity of the stars. In the case of stars with few observations, it must be computed assuming an effective temperature. Classically, the difference in bolometric magnitude is related to the luminosity ratio according to: which makes by inversion: where is the Sun's luminosity (bolometric luminosity) is the star's luminosity (bolometric luminosity) is the bolometric magnitude of the Sun is the bolometric magnitude of the star. In August 2015, the International Astronomical Union passed Resolution B2 defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power (watts) and irradiance (W/m2), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales. Combined with incorrect assumed absolute bolometric magnitudes for the Sun, this could lead to systematic errors in estimated stellar luminosities (and other stellar properties, such as radii