Fundamental Astronomy

tem objects are also observed by means of “classical”
spectroscopy.
Spectrophotometry and polarimetry give information
at discrete wavelengths only. In practise, the number of
points of the spectrum (or the number of filters available)
is often limited to 20–30. This means that no details
can be seen in the spectra. On the other hand, in ordinary
spectroscopy, the limiting magnitude is smaller,
although the situation is rapidly improving with the new
generation detectors, such as the CCD camera.
The spectrum observed is the spectrum of the Sun.
Generally, the planetary contribution is relatively small,
and these differences can be seen when the solar spectrum
is subtracted. The Uranian spectrum is a typical
example (Fig. 7.21). There are strong absorption bands
in the near-infrared. Laboratory measurements have
shown that these are due to methane. A portion of the
red light is also absorbed, causing the greenish colour of
the planet. The general techniques of spectral observations
are discussed in the context of stellar spectroscopy
in Chap. 8.
7.9 Thermal Radiation of the Planets
Thermal radiation of the solar system bodies depends
on the albedo and the distance from the Sun, i. e. on the
amount of absorbed radiation. Internal heat is important
in Jupiter and Saturn, but we may neglect it at this point.
By using the Stefan-Boltzmann law, the flux on the
surface of the Sun can be expressed as
L = 4πR 2 ⊙ σT 4 ⊙ .
If the Bond albedo of the body is A, the fraction of the
radiation absorbed by the planet is (1 − A). This is later
emitted as heat. If the body is at a distance r from the
Sun, the absorbed flux is
Labs = R2 ⊙σT 4 ⊙πR2 r2 (1 − A). (7.50)
There are good reasons to assume that the body is in
thermal equilibrium, i. e. the emitted and the absorbed
fluxes are equal. If not, the body will warm up or cool
down until equilibrium is reached.
Let us first assume that the body is rotating slowly.
The dark side has had time to cool down, and the thermal
radiation is emitted mainly from one hemisphere. The
flux emitted is
7.10 Mercury
Lem = 2πR 2 σT 4 , (7.51)
where T is the temperature of the body and 2πR 2 is the
area of one hemisphere. In thermal equilibrium, (7.50)
and (7.51) are equal:
R2 ⊙T 4 ⊙
r2 (1 − A) = 2T 4 ,
whence
1/4 1/2 1 − A R⊙
T = T⊙
. (7.52)
2 r
A body rotating quickly emits an approximately equal
flux from all parts of its surface. The emitted flux is then
Lem = 4πR 2 σT 4
and the temperature
1/4 1/2 1 − A R⊙
T = T⊙
. (7.53)
4 r
The theoretical temperatures obtained above are not
valid for most of the major planets. The main “culprits”
responsible here are the atmosphere and the internal
heat. Measured and theoretical temperatures of some
major planets are compared in Table 7.3. Venus is an
extreme example of the disagreement between theoretical
and actual figures. The reason is the greenhouse
effect: radiation is allowed to enter, but not to exit. The
same effect is at work in the Earth’s atmosphere. Without
the greenhouse effect, the mean temperature could
be well below the freezing point and the whole Earth
would be ice-covered.
7.10 Mercury
Mercury is the innermost planet of the solar system.
Its diameter is 4800 km and its mean distance from
the Sun 0.39 AU. The eccentricity of the orbit is 0.21,
which means that the distance varies between 0.31 and
0.47 AU. Because of the high eccentricity, the surface
temperature of the subsolar point varies substantially:
at the perihelion, the temperature is about 700 K; at
the aphelion, it is 100 K lower. Temperature variations
on Mercury are the most extreme in the solar system
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