Planetary Temperatures
We can calculate the temperatures that we would expect the planets to have using some simple
heat balance equations.
The total energy received over the whole of a planet is given by the area it presents to the Sun
times the radiation per square meter at that point. The radiation power per square meter at the
earth is given by S, the solar constant (around 1360 W m
2
), and we know S falls off according to
the inverse square law. Hence energy received by planet:
=
(S/a
2
)[pi]R
2
where a is the distance from the sun in AU.
Effective Temperature
, T
e
:
If a body and its atmosphere is at a uniform temperature T
e
, then it will emit as a black body
radiator of effective temperature T
e
.
Rate of emission = 4[pi]r
2
[sigma]T
e
4
where [sigma] is Stefan's Constant.
If we define the albedo as (Energy reflected)/(Total energy received), and call this A, then the
total energy absorbed is given by:
Total Energy Absorbed = [pi]R
2
S (1A)/a
2
where a = a
p
/a
e
, and a
p
is the distance of the B>p is the distance of the planet from the sun in
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 Fall '10
 EmilyHoward
 Astronomy

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