11.1.1 Calculate the Flux of a Planet

The thermal emission from a planet may be represented:

$$S_\nu = B_\nu (T) (1 - e^{-\tau}) \Omega _s$$ (11.1)

where

B$_\nu$(T)

is Planck's Law, in the Rayleigh-Jeans limit, B$_\nu$(T) = 2k$\nu^2$/c² T.

$\tau$

is the optical depth; for the planets, $\tau >>$ 1,

$\Omega_s$

is the solid angle of the source, $\pi$ $\theta_{eq}$ $\theta_{pol}$/4,

$\theta_x$

are the polar and equatorial angular diameters.

yielding,

$$S_\nu = {{2kT\nu^2}\over{c^2}} \pi \theta_s^2$$ (11.2)

The planetary diameters can be obtained from The Astronomical Almanac for the current year; for 1996, they can be found on pages E52-E77. The planetary temperatures for frequencies in the range 200-500 GHz, are summarized in Table 2.1

 

Table 11.1: Planetary Temperatures

 

Planet	Frequency	Temperature
Mercury	345	501
Venus	230	275
	345	300
Mars	230	207
Jupiter	227	171
	279	170
	337	174
	392	163
	451	167
Saturn	310	135
	451	270
Uranus	230	92
Neptune	230	88