At what distance do apparent and absolute magnitudes equal each other?

The apparent magnitude and absolute magnitude of a celestial object become equal at a distance of 10 parsecs. This is a fundamental concept in astronomy that relates the brightness of stars as observed from Earth (apparent magnitude) and their intrinsic brightness (absolute magnitude) when viewed from a standard distance of 10 parsecs.

The reason this distance is significant is based on the definition of absolute magnitude, which is the brightness of a star as it would appear if it were placed at a distance of 10 parsecs from Earth. When a star is exactly 10 parsecs away, its apparent magnitude equals its absolute magnitude. This distance serves as a convenient reference point because it allows astronomers to compare the intrinsic brightness of stars without the effects of distance altering their visibility.

At distances shorter than 10 parsecs, stars appear brighter than their absolute magnitude value would suggest, and at distances greater than 10 parsecs, they appear dimmer. Hence, the equality of apparent and absolute magnitudes happens exclusively at this benchmark of 10 parsecs.