Welcome to the second chapter of the lecture on solar radiation. In the first chapter we have learned how much energy the sun radiates into space.

In the second chapter we will take a look at what happens to the radiation as it travels from the sun to the earth. To illustrate that I would like to make a little sketch. Here we have the sun and the sun emits the radiation in all directions.

This now looks like a little children's drawing, like little children show the sun.

The radius of the sun is RS. And now here around the sun we have the orbit where the earth is circulating.

And here we have mother earth. The radius of the orbit is RSE. RSE is also called the astronomical unit, AU.

So to calculate now how much energy reaches the orbit we just have to do a very simple energy balance.

So we can assume that from the energy which is emitted by the sun all energy will reach this orbit. So we can make this little energy balance. So the energy is the product out of IS times AS.

So IS was the specific radiated power by the sun. We have learned about in the first chapter and AS is the surface of the sun. And all this energy is distributed on this orbit.

And this is then the energy density I0 on the surface of this orbit. To calculate now the energy density I'm interested in this is I0.

I solve this equation for I0 which is then IS times AS divided by 0. Now I can substitute the surface as a function of the radius. AS times 4 pi times RS squared divided by 4 pi times RSE squared.

So RS was the radius of the sun and RSE was not the radius of the earth but the radius here of this orbit.

If I put in these numbers so I know IS, I know the radius, I know the distance and then I get for I0 a value of 1367 watts per square meter.

So this is a very important number because this is a constant power which is emitted by the sun and which we can measure here on this orbit here.

So we have this radiation continuously on this orbit. However depending on which side on the earth you are, so if you are on this side you have day time and

you see this radiation or if you are on the other side you have night time and you don't see this radiation. But on the path here facing the sun we have this radiation continuously non-stop and constant and therefore this value is also called the solar constant.

So this is the radiation intensity you have on this orbit and consequently also on earth but to be very precise this is not the radiation on the surface of the earth but it is on

the outside of the atmosphere of the earth and therefore this radiation is also called the extraterrestrial radiation. So and as the sketch clearly shows and as also the equation here clearly

shows that this value depends just on the distance between the earth and the sun. So a planet which is closer to the sun sees a higher radiation than a planet which is farther away from the sun.

May be obvious but very important to keep in mind. As just stated the solar constant depends on the distance between sun and earth which is about 150 million kilometers. But unfortunately this distance is not really constant.

You all know that the earth does not orbit the sun on an exact circular path but on an ellipse. Therefore the distance between the earth and the sun is not really constant and depends on the position of the earth on this elliptical orbit.

This means that the famous solar constant is not really a constant. The value of 1367 watts per square meter is the average value which was calculated for the average distance of 150 million kilometers. And the fluctuating distance between the earth and the sun also results in the fluctuation of this extraterrestrial radiation over the year.

Let's have a look at this little illustration here on the right. The earth is closer to the sun when it is at this position here. This is in January and then the distance is only 147 million kilometers.

And in July the sun is further away from the earth and the distance is 152 million kilometers. Consequently the value for the extraterrestrial solar radiation will be a little lower in July when the

earth is further away from the sun than in January when the earth is closer to the sun. You might have expected that this is the other way around since we observe higher temperatures in summer than in winter. But this is actually not the case as we see in this illustration.

Why we nevertheless observe lower temperatures in winter than in summer, this we will discuss in the next chapter. So when I have just mentioned summer and winter I of course refer to the northern hemisphere.

In the southern hemisphere it is obviously the other way around and in July it is winter and in January it is summer. On this slide an equation is presented to calculate the exact value for the extraterrestrial radiation. The value depends on the day of the year which is described by the parameter j.

And on the right side we see a graph depicting this equation that shows the variation of the solar constant depending on the day of the year or respectively the month of the year. As you can see in this graph the radiation varies from 1320 watts per square meter which we observe in summer

when the earth is far away from the sun up to a value of 1412 watts per square meter which we have in winter when the earth is closer to the sun as it can be seen right now here in this illustration.

With this I come to the summary of the second chapter. The solar radiation that reaches the earth only depends on the distance between sun and earth. The extraterrestrial radiation is called the solar constant I0 with a value of 1367 watts per square meter.

Depending on the season which means on the position of the earth on the orbit and consequently on the actual distance between sun and earth this value can vary in the range of plus minus three percent.

In the next chapter we will then learn what happens to the radiation on the next part of its journey to the surface of the earth.