Calculating Surface Brightness
Surface brightnesses are usually quoted in magnitudes per square arcsecond. Because the magnitude is logarithmic, calculating surface brightness cannot be done by simple division of magnitude by area. Instead, for a source with magnitude m extending over an area of A square arcseconds, the surface brightness S is given by
Surface brightness is constant with luminosity distance. For nearby objects, the luminosity distance is equal to the physical distance of the object. For a nearby object emitting a given amount of light, radiative flux decreases with the square of the distance to the object, but the physical area corresponding to a given solid angle (e. g. 1 square arcsecond) increases in the same fashion, resulting in the same surface brightness.
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—J.G. (James Graham)
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