Narration script

Unit six. We now follow sunlight across space. Above the atmosphere, sunlight arrives at about thirteen hundred and sixty-one watts per square metre on a surface facing the Sun. You can derive that number yourself from the Sun's temperature, its size, and its distance. The spectrum out there is called A M zero, air mass zero, and it is the standard for space solar cells, which makes it directly relevant to satellite solar work like Starlink.

You will derive the solar constant, explain why it varies by about three percent through the year, describe the A M zero spectrum, and explain why space cells are rated under a different spectrum from rooftop panels.

A M zero is the starting point from which the atmosphere carves the ground spectrum, and it is the everyday operating spectrum for satellites. Space arrays are tested under A M zero simulators and must also survive radiation and thermal cycling.

Here is the derivation. The Sun's total output is its surface area times sigma T to the fourth, from the Stefan-Boltzmann law. At Earth's distance, that output is spread over a giant sphere whose radius is the Earth-Sun distance. Divide one by the other and the four pi's cancel. The irradiance is the Sun's surface brightness times the square of the Sun's radius divided by the distance.

This picture shows the idea, not to scale. The same power spreads over larger and larger spheres. That is the inverse-square law: double the distance, and the irradiance drops to a quarter.

Now the numbers. Sigma T to the fourth at fifty-seven seventy-two kelvin is about sixty-three million watts per square metre. The Sun's radius divided by one astronomical unit is about four point six five thousandths, and squared that is about two point one six times ten to the minus five. Multiply, and you get about thirteen hundred and sixty-one watts per square metre. That matches the satellite measurement. From three numbers and one law, we have predicted the brightness of sunlight in space.

Satellites measure this directly as total solar irradiance. The modern value, from Kopp and Lean in twenty eleven, is thirteen sixty point eight, plus or minus zero point five watts per square metre at solar minimum. It changes only about zero point one percent over the eleven-year sunspot cycle. Older references and the space standard use about thirteen sixty-six, so expect to see both.

Earth's orbit is slightly elliptical, so our distance from the Sun changes through the year.

This curve shows the result: about three point three percent above average in early January, at perihelion, and three point three percent below in early July. Notice the surprise. Northern-hemisphere winter is when Earth is closest to the Sun. Seasons are caused by the tilt of Earth's axis, not by distance.

You may also see the number three hundred and forty watts per square metre. That is thirteen sixty-one divided by four, because Earth intercepts sunlight on a disc but has four times that area as a sphere. Climate scientists use the average. Solar engineers care about the full value on a surface facing the Sun.

The A M zero spectrum is tabulated in standards. The extraterrestrial column of the A S T M G one seventy-three table, which we use on this site, covers two hundred and eighty to four thousand nanometres and integrates to about thirteen forty-eight watts per square metre. That is a bit less than the total, simply because the shortest and longest wavelengths are not included in the table. Compared with sunlight on the ground, A M zero has much more ultraviolet and blue, and no water-vapour gaps.

One more property: the Sun's disc spans only about half a degree in the sky. So sunlight is nearly parallel. That is why lenses and mirrors can concentrate it, in theory up to about forty-six thousand suns, and why direct and diffuse light behave so differently once the atmosphere starts scattering.

Satellites see A M zero continuously while in sunlight, so space cells are calibrated against it, using reference cells calibrated on high-altitude balloons or aircraft. A M zero is about thirty-six percent brighter than the one thousand watt terrestrial standard and bluer, so the same cell gives different efficiency numbers under the two conditions. Always check which spectrum an efficiency refers to.

Here is an illustrative example. A four square centimetre cell delivering zero point one two four watts under A M zero is twenty-two point eight percent efficient. Under the ground standard it might deliver zero point zero nine eight watts, which is twenty-four and a half percent. More power in space, lower rated efficiency, and no contradiction, because the spectra differ.

Misconceptions. Summer is not hot because we are closer to the Sun. The solar constant is not perfectly constant. Thirteen sixty-one, thirteen sixty-six and thirteen forty-eight are not contradictions; they refer to different measurements and wavelength ranges. And space cells are not always more efficient; they get more power, but often a lower rated efficiency, and they degrade from radiation.

For the job: space solar manufacturing tests cells under A M zero simulators and qualifies them for radiation and thermal cycling. Calibration chains exist for both space and ground spectra. And the extra ultraviolet in space drives choices of cover glass and adhesives.

Work the review questions, including recomputing the solar constant from scratch. In the next unit, sunlight enters the atmosphere, and we will see how the air reshapes it into the ground spectrum used for every rooftop panel datasheet.