
The Relationship Between Flux and Brightness TemperatureIn the following we derive the relationship between the flux of a source and its brightness temperature for a gaussian beam measuring two different source geometries, uniform disk and gaussian. The general relation between flux and brightness temperature is
Note that throughout this discussion when we refer to a “temperature” we are actually referring to the effective source radiation temperature J(ν; T), which is defined by Equation C.1.
where we have used the fact that
Plugging in some constants into Equation B.2 yields the following
The peak flux densities of the planets are calculated by the planets program using Equation B.6.
B.2 Elliptical Gaussian Source
Plugging in some constants into Equation B.7 yields the following

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