Absolute Magnitude

by Dominic Ford, Editor

Deep sky objects

\[ m = M + 5 \log d_\textrm{pc} - 5 \] Distance modulus \(\mu\) is defined as \[ \mu = 5 \log d_\textrm{pc} - 5 \] Distance \(d_\textrm{pc}\) is measured in parsecs.

Asteroids

\[ m = g + 5 \log \Delta + \kappa \log d_\textrm{S} - 2.5 \log p \] where \[ p=\frac{1 + \cos\beta}{2}, \] \( \beta \) is the phase angle – the Sun-Body-Earth angle, and
\( p \) is the fraction of the object's visible disk which is illuminated by the Sun. \( \kappa = 2.5 n \)

In 1985, the International Astronomical Union's Commission 20 adopted a more flexible formula, of the form \[ m = H + 5 \log d_\textrm{E} - 2.5 \log \left( (1-G)\Psi_1 + G\Psi_2 \right) \] where: \[ \Psi_1 = \exp \left[ -3.33 \left( \tan \frac{\beta}{2} \right)^{0.63} \right] \] and \[ \Psi_2 = \exp \left[ -1.87 \left( \tan \frac{\beta}{2} \right)^{1.22} \right] \] the brightness of an asteroid is defined by its absolute magnitude \(H\), and its slope parameter \(G\). All distances measured in astronomical units. See chapter 33 (page 231) of Astronomical Algorithms (1991) by Jean Meeus.

Comets

\[ m = g + 5 \log d_\textrm{E} + 2.5 n \log d_\textrm{S} - 2.5 \log p \] where, as above, \[ p=\frac{1 + \cos\beta}{2}, \] \( \beta \) is the phase angle – the Sun-Body-Earth angle, and
\( p \) is the fraction of the object's visible disk which is illuminated by the Sun.

Cambridge

Latitude:
Longitude:
Timezone:

42.38°N
71.11°W
EDT

Color scheme