# Brightness Temperature

Brightness temperature is the temperature a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a frequency . This concept is extensively used in radio astronomy and planetary science.

For a black body, Planck's law gives :

where

(the Intensity or Brightness) is the amount of energy per unit surface per unit time per unit solid angle emitted in the frequency range between and, is the temperature of the black body, is Planck's constant, is frequency, is the speed of light and is Boltzmann's constant.

For a grey body the spectral radiance is a portion of the black body radiance, determined by the emissivity . That makes the reciprocal of the brightness temperature:

At low frequency and high temperatures, when, we can use the Rayleigh–Jeans law:

so that the brightness temperature can be simply written as:

In general, the brightness temperature is a function of, and only in the case of blackbody radiation is it the same at all frequencies. The brightness temperature can be used to calculate the spectral index of a body, in the case of non-thermal radiation.

### Famous quotes containing the words brightness and/or temperature:

For pain is perhaps but a violent pleasure? Who could determine the point where pleasure becomes pain, where pain is still a pleasure? Is not the utmost brightness of the ideal world soothing to us, while the lightest shadows of the physical world annoy?
Honoré De Balzac (1799–1850)

This pond never breaks up so soon as the others in this neighborhood, on account both of its greater depth and its having no stream passing through it to melt or wear away the ice.... It indicates better than any water hereabouts the absolute progress of the season, being least affected by transient changes of temperature. A severe cold of a few days’ duration in March may very much retard the opening of the former ponds, while the temperature of Walden increases almost uninterruptedly.
Henry David Thoreau (1817–1862)