## 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 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:

(1)

and are the apparent major and minor axis of the planet ( being the planet radius and the geocentric distance in km). 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, 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) |  |  |