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:

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