# The Naked Scientists Forum

### Author Topic: So what is the output of the Sun relative to the heat we receive on Earth?  (Read 3571 times)

#### damocles

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##### So what is the output of the Sun relative to the heat we receive on Earth?
« on: 19/02/2012 00:36:12 »
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So what is the 'output' of the sun relative the heat/IR we receive on Earth? I guess it might be difficult to answer that one but it would be interesting to know the relation between those two. If we talk about photons the only way they 'annihilate' is through interactions, if we talk about waves we have quenching and reinforcing. And the waves from the sun are polychromatic, of a lot of different wavelengths. So how do the transfer of heat works, and if some get lost, to what does it lose?

In some ways the answer to that one is surprisingly easy! When it reaches the Earth, the total radiation output of the Sun is, to a good approximation, uniformly spread over the surface of a sphere with radius equal to the distance from Sun to Earth -- roughly 150 million km. The total surface area of this sphere is 4 x π x (1.5E11)2 m2 = 2.8E23 m2.

The cross-section area of the Earth's disk that intercepts some of this light is given by π x (radius of Earth)^2, and the radius of the Earth is around 6500 km.

π x (6.5E6)2 m2 = 1.33E14 m2.

The proportion of the total solar output that is intercepted by the Earth is therefore 1:2E9 -- about one two billionth!

When the Earth intercepts solar radiation, there are lots of complicated physical and chemical processes that might follow, but they really amount to two things -- either the radiation is absorbed somewhere in the Earth system, or the radiation is reflected back into space. The proportion that is directly reflected is known as the "albedo", and the Earth's albedo is around 36%. The other 64% is absorbed and used by various Earth systems. As usual the actual situation is just a little more complicated because the albedo is wavelength dependent -- the reflection/absorption balance differs for different wavelengths of solar radiation.

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That is a fairly complete simple answer, but it is really necessary to expand it with a summary of the rest of the story. Obviously the Earth does not just keep on absorbing solar radiation, or it would just keep getting hotter and hotter! The Earth (and any other hot body) radiates on its own account, and in doing so it loses energy and cools itself. A balance is reached when the heat gain from absorbing solar radiation is exactly matched by the emission of the Earth's own radiation.

The hotter a body is, the more power output, and the shorter the wavelength average of its radiation spectrum. A metal looks black when we can feel its infrared radiation, but if it gets a little hotter we will see it radiate visible red light (red hot), and at higher temperatures yellow, and then white light.

The sun's radiation is mostly in the visible region, with a peak output in the green part of the spectrum -- near the middle of the visible. That is a wavelength of about 0.52 µm. The Earth's radiation is infrared, with a peak wavelength around 16 µm. Emission of radiation is governed by the same albedo factor as absorption: the more reflection and the less absorption, the less the emission will be.

The normal average surface temperature of a planetary body at the Earth's position in the solar system can fairly readily be calculated: it works out at -20°C, and that is roughly correct for the moon. The Earth is (fortunately) warmer, with an average surface temperature of 16°C, as the result of several complicating factors. The most important of them arises from the presence of water clouds, and water vapour in the atmosphere.
« Last Edit: 19/02/2012 00:57:45 by chris »

#### syhprum

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##### Re: So what is the output of the Sun relative to the heat we receive on Earth?
« Reply #1 on: 19/02/2012 07:10:43 »
With a theoretical surface temperature of -20°C could the Earth be said to be in the "goldilocks zone" or just outside it ?.

#### Soul Surfer

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##### Re: So what is the output of the Sun relative to the heat we receive on Earth?
« Reply #2 on: 19/02/2012 09:51:21 »
Any planet with an atmosphere will experience a certain amount of greenhouse effect and be slightly warmer than the mean vacuum temperature.  The most important feature of an atmosphere and clouds is to smooth out the temperature fluctuations although the average may be around -20  the temperature difference between the sunny side and the shaded side is around 400 degrees c  that is around +180 on the sunny side and  -220 on the shady side exposed to the near absolute zero of space and the day night temperatures in the moon are as extreme as this

#### yor_on

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##### Re: So what is the output of the Sun relative to the heat we receive on Earth?
« Reply #3 on: 19/02/2012 20:40:19 »
A nice thread all, and thanks Damocles :)

All waves can be considered to carry heat, which should be the same as 'energy', if I'm thinking right here, and the reason why some waves are more usual on earth (IR) is a direct result of their black body spectrum (heat content). Can I assume that all wavelengths find it as 'easy' to propagate through space? It seems to me that there is a difference if we look at radio wavelengths for example?

What I'm wondering about is how, and if, all that suns output (wavelengths) are received here? And the reason to why it won't reach us, if so? It's just some half-baked question so far, it's nagging on me but I don't really know why yet.

#### Bored chemist

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##### Re: So what is the output of the Sun relative to the heat we receive on Earth?
« Reply #4 on: 19/02/2012 21:05:10 »
Some reaches us but is reflected (especially by the clouds and ice). All the EM radiation travels through space with no problem.
Some must get scattered by the very thin gas between us and the sun.

#### yor_on

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##### Re: So what is the output of the Sun relative to the heat we receive on Earth?
« Reply #5 on: 19/02/2012 22:23:15 »
Thanks for that BC. It's photons from a particle view, and those are expected to have a infinite reach, as observed by us. But when it comes to waves some seems to be able to penetrate fluids and solids, like those used to transmit to submarines. Can one explain that with a particle picture, or is it solely a wave view that works?

#### The Naked Scientists Forum

##### Re: So what is the output of the Sun relative to the heat we receive on Earth?
« Reply #5 on: 19/02/2012 22:23:15 »