Physics question.

In message , Sleepalot
writes
Stewart Robert Hinsley wrote:

You could start from the solar constant. From this you can get an
estimate of the downward flux of photons from the sun. Let a be the
albedo of the Earth's surface. Let N be the downward flux. The downward
and upward energy fluxes must balance. Ignoring the greenhouse effect,
and the internal heat generation of the earth, the total flux of photons
is [(1+a) + x(1-a)]N, where x is the ratio of the energy of incoming
light and outgoing heat photons (finger in the air, x is about 10,
giving [1+a+x-ax]N = [1+x-a(x-1)]N. That comes out at about 8N.

Sorry Stewart, I'm out of my depth here. You seem to be saying
that there are (perhaps) 8 times as many photons going out (with
lower energies) as coming in. Have I got that right?


Yes, with caveats.

The energy reaching the surface of the Earth from the Sun is dominated
by visible and near infrared wavelengths, because

1) that's where the peak of the solar energy production is
2) radiation at many other wavelengths is absorbed by the atmosphere.

The same amount of energy, plus a small contribution from the internal
heat production of the Earth, must leave the surface of the Earth. Some
is just reflected. Some heats the surface. Some of this heat is carried
away by convection (and subsequently radiated by the atmosphere), and
some is radiated, at considerably longer wavelengths and lower energies,
with a consequent increase in the number of photons.

Because of absorption of infra-red radiation by the atmosphere there's
also an incoming flux of infra-red photons reradiated by the atmosphere.
This why I specified ignoring the greenhouse effect.

The other caveat is while the solar energy flux is dominated by visible
and near-infrared wavelengths this doesn't mean that the solar photon
flux is. AM radio wavelengths are a trillion times longer than visible
light wavelengths, so the solar energy flux has to be very small for the
photon flux at those wavelengths to be negligible.

A bit of googling suggests that it is indeed negligible.
--
Stewart Robert Hinsley