apparent magnitude — from formula anatomyApparent magnitude is a measure of how bright a celestial object appears from Earth, on a logarithmic scale. It is a historical yet still widely used system in astronomy to compare the brightness of stars, planets, and other objects as seen by an observer. The scale is inverted: lower numbers mean brighter objects, with the brightest stars having negative magnitudes and the faintest detectable objects having magnitudes around 30.
The system was formalized by the Greek astronomer Hipparchus in the 2nd century BCE, who classified stars into six brightness classes. It was later given a mathematical basis by Norman Robert Pogson in 1856, who established the logarithmic relationship that is still used today.
The scale is defined such that a difference of 5 magnitudes corresponds to a brightness ratio of exactly 100. Each magnitude step is a factor of the fifth root of 100 (about 2.512) in brightness. The apparent magnitude depends on both the object's intrinsic luminosity and its distance, as well as any interstellar absorption. It is calibrated using standard reference stars, and modern measurements use photometric filters to define specific wavelength bands.
Apparent magnitude is used in observational astronomy to catalog stars, plan telescope observations, and estimate distances via the distance modulus when combined with absolute magnitude.
The Sun has an apparent magnitude of about −26.7, while the faintest objects observed by the James Webb Space Telescope have magnitudes around 30, making the Sun about 10^22 times brighter than the faintest detectable objects.
| m | variable | apparent magnitude — apparent magnitude |
| M | variable | absolute magnitude — absolute magnitude |
| d | variable | distance to the object — distance parsec |
| log10 | operator | base-10 logarithm — logarithm base 10 |
| m | variable | apparent magnitude — apparent magnitude |
| H | variable | absolute magnitude — absolute magnitude |
| d | variable | distance to the object — distance parsec |
| \text{phase correcti | variable | correction for phase angle (e.g., for planets or asteroids) — phase correction |
| \log_{10} | operator | logarithm to base 10 — logarithm base 10 |
| M_{\rm ext} | variable | Observed apparent magnitude — apparent magnitude |
| M_{\rm int} | variable | Intrinsic apparent magnitude — apparent magnitude |
| A | variable | Extinction in magnitudes — extinction |










