Planet flux computation

In ASTRO the planets are defined as ellipses. The planet flux computation is based on a surface averaged brightness temperature at the considered frequency. The flux is then obtained using this brightness temperature $T_B$ in the Planck function and integrating this brightness over the planet apparent surface (which depends on the distance to the Earth) according to the equation:

  $\displaystyle F(\nu) = \pi\,\theta_{maj}\,\theta_{min} \, \frac{2\,h\,\nu^{3}}{...
...{1}{e^{\frac{h \nu}{k T_B}}-1} - \frac{1}{e^{\frac{h \nu}{k T_{BG}}}-1}\right]
$ (1)

$\theta_{maj} = \frac{R_{Maj}}{\Delta}$ and $\theta_{min} = \frac{R_{Min}}{\Delta}$ are the apparent major and minor axis of the planet ($R$ being the planet radius and $\Delta$ the geocentric distance in km). $T_{BG}$ is the cosmic background radiation (2.7 K)

We list in Table 1 the brightness models used in the original ASTRO implementation (Legacy models), the models we propose to implement (2024), and the models used in CASA.


Table 1: Planet brightness models in ASTRO and CASA
Planet ASTRO Legacy ASTRO 2024 CASA      
Mercury Flat Spectrum Flat Spectrum No model      
      (too close to the Sun)      
Venus Spectral Index Spectral Index Physical model      
      Clancy et al. 2012      
Mars Flat spectrum, $r_h$ scaling Physical model Physical model      
    Lellouch et al. Butler et al.      
Juptier Flat spectrum Physical model Physical model      
    ESA2 (R. Moreno) ESA4 (G. Orton and R. Moreno)      
Saturn Flat spectrum Physical model No model      
    ESA2 (R. Moreno)        
Uranus Spectral index Physical model Physical model      
    ESA2 (R. Moreno) ESA4 (G. Orton and R. Moreno)      
Neptune Spectral index Physical model Physical model      
    ESA5 (R. Moreno) ESA3 (G. Orton and R. Moreno)