Calculating Mars' brightness temperatures

For Mars, the brightness temperature at each filter wavelength is calculated via a logarithmic interpolation between brightness temperatures at 350$\mu$m (857 GHz), $T_{b_{857}}$, and another at 3.3mm (90 GHz), $T_{b_{90}}$. The first of these is generated from one of two models both from Wright's work, the results of which are held as an array in FLUXES. In the array, values for $T_{b_{857}}$ are given at 40-day intervals, and so a linear interpolation is performed to ascertain a value for the given date.

The 3.3mm point is calculated from the relation given by Ulich (1981, A.J., 86, 1619):

$$T_{b_{90}} = \frac{206.8}{\sqrt{1.524/d_{hel_{Mars}}}}$$

where 1.524 AU is the mean heliocentric distance of Mars and $d_{hel_{Mars}}$ is the heliocentric distance of Mars for the given date, which can be calculated from the precessed geocentric positions and distances of the Sun ( ${RA^\prime}_{g_{sun}}$, ${Dec^\prime}_{g_{sun}}$, $d_{g_{sun}}$) and Mars ( ${RA^\prime}_{g_{Mars}}$, ${Dec^\prime}_{g_{Mars}}$, $d_{g_{Mars}}$) by defining the following quantity:

$$\cos E = \sin {Dec^\prime}_{g_{Mars}} \sin {Dec^\prime}_{g_{... ...g_{sun}} \cos ({RA^\prime}_{g_{sun}} - {RA^\prime}_{g_{Mars}})$$

so that

$$d_{hel_{Mars}} = \sqrt{{RA^\prime}_{g_{sun}}^2 + {RA^\prime}... ...}}^2 - 2 (\cos E){RA^\prime}_{g_{sun}}{RA^\prime}_{g_{Mars}}}.$$

Thus the brightness temperature at a given frequency, $\nu$ GHz, is given by a logarithmic interpolation:

$$T_{b_\nu} = T_{b_{90}} + (T_{b_{857}} - T_{b_{90}})\frac{\ln(\nu - 90)}{\ln(857 -90)}$$