15 Million Degrees

by Lucie Green

  For now, one way to reconcile this apparent contradiction is to think of a beam of light as actually being made of countless individual flashes of light, which we call ‘photons’ – as if a torch were being switched on and off very quickly. The wave is then an average over the countless flashes of light.

  As you sit in the sunlight, this energy is continually falling on you thanks to the vast number of photons of all different wavelengths that the Sun continuously emits. Every square metre of the Earth is being bombarded by 100 billion billion photons every second, which together deliver 1000 joules of energy – about the same energy as is used every second by a microwave oven. And over the sunlit side of the 510 million million square metres of the Earth’s surface this really adds up. Some of this energy is reflected back into space but some of it goes into heating our oceans and atmosphere and powering modern society. Our knowledge of all this came from understanding what light actually is. Maxwell’s work can perhaps be considered the greatest scientific achievement of the nineteenth century.

  So the question now is: how does the Sun create sunlight? And where does all this energy come from?

  2. Star Power

  The Sun arises in the East,

  Cloth’d in robes of blood and gold;

  Swords and spears and wrath increast

  All around his bosom roll’d

  Crown’d with warlike fires and raging desires.

  William Blake, ‘Day’

  Looking back into antiquity, we see two themes linked with the Sun: fire and power. In his poem ‘Day’, the English poet William Blake takes them up, talking about the Sun in terms of a warlike and menacing fire and anthropomorphizing our star as a warrior king with a flaming crown and powerful feelings. Well before Blake, the Aztecs, who lived in central Mexico 500 years ago, had Xiuhtecuhtli, their deity of both day and light and of fire. The Chinese had their Sun god, Yang, also made of fire.

  Perhaps fire, flame and burning feature somewhere in your visceral feelings about the Sun too. From our everyday experience of the Sun’s light and warmth, it’s hard not to think of fire when we try to describe and understand the Sun. It might surprise you to know that this way of thinking isn’t reserved just for the arts: scientists have thought along these lines too. The defining aspect of our Sun is that it shines – it makes its own light. And it’s hard not to equate this with the most familiar example of light and heat we have here on Earth: a roaring fire.

  The idea that fire is the reason why the Sun shines was considered as recently as the early nineteenth century. Against the backdrop of the Industrial Revolution, it was pondered whether a large enough coal fire might be able to provide the vast amount of light we receive from the Sun. It’s an alarming thought: once all the coal was burnt, the Sun would go out; perhaps an early end-of-the-world scenario. But that was the same insight we could use to test the theory: the Sun has been burning for a long time and it hasn’t gone out yet. How much coal would it have required so far?

  To even begin to answer that question, scientists needed a coherent theory of energy. There is energy stored in coal, and by burning it that energy is freed and somehow converted into light and heat. But to even discuss energy as a quantity that can be measured, and as something that can be used, requires some serious advances in thinking. Thankfully the energy-hungry Industrial Revolution provided the motivation to achieve an understanding of energy. Unfortunately, the first step towards this understanding sounds hugely antiquated, and perhaps even racist, to our modern ears.

  Julius Robert Mayer was a German doctor and amateur scientist. In 1840 he was travelling to Java, working as a ship’s surgeon, when he had a strange epiphany. As he went about a nineteenth-century physician’s duties such as letting blood, he noticed that the blood in the veins of the sailors who lived in warmer countries was more vividly red than that of his fellow Germans. He also relied on fire for his explanation of energy. He hypothesized that when food was ‘burnt’ in the body, it produced dark ash that went into the blood. If the body burnt more food, it would produce more ash and the blood would appear a darker red. Mayer speculated that sailors from warmer countries had vividly red blood because their bodies didn’t need to use as much food to keep warm, and so didn’t produce as much ash in the blood as sailors from colder countries.

  We would find Mayer’s physiological reasoning faulty today, but back then the analogy of fire equating to energy and warmth prevailed. The stroke of genius came when Mayer started thinking about other ways for the body to keep warm: for example, by rubbing your hands together. This gives the same result as a situation Mayer would have been familiar with on ships: when a rope runs through your hands it causes rope-burn – friction causes things to get hot. And, most obviously, physical labour, like swabbing decks and whatnot, would warm someone up too. By observing this line of cause and effect – food provides warmth for the body and so does doing work – Mayer arrived at a radical conclusion: mechanical work and heat were both being derived from a single quantity – energy – and this quantity could be transferred from one place to another but was always conserved. The overall amount of energy didn’t change.

  In England, meanwhile, James Prescott Joule, the son of a wealthy brewer, was working in Manchester, the city at the very heart of the Industrial Revolution. And central to the Industrial Revolution were investigations and experiments looking at heat and energy. The units we now use to measure energy bear his name, so it lives on all around us. I have a bag of corn chips on my desk as I write, and on the back it says that each 100 grams contains 2035 kilojoules. This is the amount of energy that can be extracted from the chips by my body when I digest them. I know that each 100 grams of chips contains 2,035,000 joules of energy. A frightening thought!

  Joule’s experiments led him to the same conclusion as Mayer, although they had very different approaches. In one experiment, Joule constructed a mechanism where a gradually falling weight pulled on a rope that moved a paddle and stirred some water. As the water was stirred its temperature went up: the mechanical energy of the paddle (derived from the potential energy of the weight) was turned into heat, showing that the mechanical energy of the paddle was equivalent to the energy of the heat. Again, energy had been transferred from one place to another.

  The work of these two men was key in establishing a law that has become known as the First Law of Thermodynamics, which has at its heart the conservation of energy: energy can be neither created nor destroyed. Instead, it can only change from one form into another. This development in scientific understanding was so important that a bitter dispute took place between the leading scientists of that time about who could take the credit for its discovery. They argued publicly; it was a matter of national pride with Joule and Britain being set against Mayer and Germany. In what could be seen as a conciliatory gesture the Royal Society awarded the most prestigious medal to Joule in 1870 for his ‘experimental researches on the dynamical theory of heat’ and to Mayer in 1871 for his ‘researches on the mechanics of heat’.

  Nineteenth-century experimentation also showed that to raise the temperature of 1 gram of water by 1 degree Celsius requires just over 4 joules of energy. Knowing this meant we could start to measure how much energy the Sun is producing. If you leave a known amount of water out in direct sunlight when the Sun is directly overhead and measure how long it takes to raise the temperature you can use this formula to calculate the rate at which the Sun’s radiation transfers energy to heat the water. By the late 1830s, this had been done independently by the French physicist Claude Pouillet and the English astronomer John Herschel.

&nb
sp; John Herschel became interested in the Sun’s energy for rather personal reasons. In a tradition maintained by English tourists overseas to this very day, he was severely sunburnt during a trip across the Alps in 1825. John Herschel was also the son of the famous astronomer William Herschel (who discovered Uranus*) and he was a successful astronomer in his own right. He took up astronomy rather late in life, continuing his father’s work when he became too frail to do the work himself. After almost twenty years of working in astronomy, John then moved his family to South Africa to survey the skies of the southern hemisphere, where he catalogued stars and nebulae. He even made observations of Halley’s comet when it became visible in 1835 and he realized that the heat of the Sun was causing cometary material to vaporize.

  But Herschel wasn’t the only person interested in the amount of energy delivered in sunlight. Claude Pouillet developed a new instrument that could measure the energy delivered in sunlight. He called this new instrument a ‘pyrheliometer’. Herschel and Pouillet’s experiments provided a way to measure the amount of energy falling on the very small surface area of their vessels of water. This value could be scaled up to find the energy falling on every square metre of the Earth. But it isn’t the amount of energy that is falling on ground that is important if we want to calculate how much energy the Sun is emitting. Sunlight only reaches the surface of the Earth after having passed through the atmosphere, and that reduces its intensity. The amount reaching the upper limit of the atmosphere is more than that measured on the ground – their calculations gave a figure of 1260 joules per second per square metre.

  Nowadays we have the ability to put instruments on satellites and make measurements above our atmosphere directly, and it turns out that Herschel and Pouillet were not too far off the actual figure of 1361 joules per second per square metre. In the units used by my corn chips, that’s around 1.4 kilojoules. This is equivalent to about 0.1 grams of corn chips every second per square metre, which certainly does not sound like much. But this is just the rate of energy that falls on a relatively small area. To work out how much energy the Sun is emitting in all directions every second requires us to think big.

  Imagine a huge sphere that it is centred on the Sun and extends out to the distance of the Earth, 150 million kilometres from its centre. Now visualize light flooding out from the Sun in all directions onto every part of the sphere. We know from the measurements at the Earth that every square metre receives 1361 joules per second, so to calculate the total amount of energy falling on the sphere we must multiply 1361 joules by the sphere’s total surface area. This gives us an incredible value of 4 × 1026 joules every second (400,000,000,000,000,000,000,000,000 joules). The Sun produces the energy of around 20 million billion tonnes of corn chips a second. Because it is blasting out in all directions into space, this is over two billion times the amount we receive at the Earth. It is the amount of energy that the Sun radiates every second and this is the amount that whatever process is powering the Sun must be able to provide. So now we are in a position to answer the question: could the Sun be powered by burning coal?

  Coal is comparable to corn chips: 100 grams of my chips can provide approximately 2000 kilojoules, 100 grams of coal can supply 1000 kilojoules (but tastes substantially worse). Burning 1 kilogram of coal releases 10,000 kilojoules of energy, but, still, this is a minuscule amount compared to the amount that the Sun is emitting. Even the most powerful coal-burning power station today would have to run constantly for thousands of billions of years to produce as much energy as the Sun does in one second. When you know the numbers, coal starts to look like a pretty measly energy source. Clearly a large amount would be needed to allow the Sun to shine so brightly. And, not only that, but the Sun would have to be massive enough to keep itself shining this brightly during its lifetime. Which brings us to an interesting detour: how massive would our theoretical coal-burning Sun need to be? And is the Sun bigger or smaller than that? If the Sun is smaller than that, we can rule that fuel out. But calculating the Sun’s mass is not a short detour.

  CRITICAL MASS

  Calculating the mass of something as distant as the Sun is no easy feat. The first step in the right direction is thanks to our old friend Isaac Newton. Not just content with shining light through prisms and arguing with Hooke, he is also famous for discovering the law of gravity, apparently after having been inspired by an apple (150 kilojoules per 100 grams).

  In 1687 he published his Philosophiæ Naturalis Principia Mathematica, which laid out a set of equations describing how objects move when they are and aren’t being acted on by a force, and how an object that is stationary will stay at rest unless it is moved by a force. This includes celestial bodies, such as the planets, and how they move under the force of gravity. This describes yet another force acting at a distance, highly controversial at the time, which pulls two objects together with a strength that is dependent on their mass and separation from each other and nothing else.

  As fundamental forces go, gravity is pretty weak. But the beauty is it works over vast distances. Newton had been inspired by the work of an earlier German mathematician and astronomer, called Johannes Kepler. In 1619 Kepler had published his finding that the time it took a planet to orbit the Sun is related to its distance from it. Newton expanded Kepler’s observational work using his newly developed theory to provide a description of how planets move that involves the mass of the Sun and the mass of the planet. These theories take us most, but not all, of the way to working out the mass of the Sun. We need to put some numbers into the equations.

  In fact, only one number is needed: the distance of a planet from the Sun – any planet will do. Despite having all the necessary equations in the seventeenth century, Newton didn’t have this one numerical key that would unlock the problem of the mass of the Sun. It took until the eighteenth century for scientists to be able to calculate how far the Earth was from the Sun, but the delay wasn’t in waiting for someone like Maxwell or Joule to come along and find a solution – we were waiting on the Sun itself, specifically that rare celestial occurrence: the transit, from the Earth’s point of view, of Venus in front of the Sun.

  We see a transit of Venus approximately every 115 years, when a pair of transits occur eight years apart. The first transit of Venus ever to be witnessed by human eyes didn’t happen until 1639. Planetary motions were understood well enough by then to be able to predict that year’s transit and two people in the know in Britain had skies clear enough to see it. By 1716 the British astronomer Edmond Halley (more famous for his work on cometary orbits) had worked out how to use a transit of Venus to calculate the distance to the Sun accurately. But the next transits of Venus were not until 1761 and 1769. Halley knew that he would not live to see these events and urged that the message be passed down so that astronomers alive then would make observations. Thankfully they did and calculated the distance between the Sun and the Earth to be between 92 million and 96.1 million miles.

  Then, a small amount of number-crunching later, it was calculated that the Sun has a whopping mass of 2 × 1030 kg, which is 1000 times more massive than all the planets put together and 333,000 times the mass of the Earth. Knowing that one kilogram of coal releases 10 million joules of energy, we can calculate that a pile of coal the size of the Sun would release 2 × 1037 joules. At the current rate the Sun is blasting energy into space, that stockpile would only last for 6300 years.

  Despite the persistence even today of a small ‘young Earth’ cult, we now know that the Sun has been around for 4.6 billion years. There is no flammable fuel that could possibly be keeping the Sun going over this kind of time period. So if
the energy source of the Sun is the very material of which it is made, and it is made of coal, it is simply not massive enough. Despite the Sun being synonymous with fire for all of human history, we can now say that the Sun is definitely not on fire. In the mid-1800s a more plausible theory was popular – that comets and asteroids falling into the Sun provided the energy source as the energy of motion of the incoming bodies was converted to heat. This idea fell by the wayside, though, when, despite over two centuries of telescopic observations, no comets or asteroids had been seen raining down on the Sun. A related alternative theory was that the Sun was shrinking and releasing energy from its own infall. The surface of the Sun would need to drop by just 35 metres per year to provide enough energy but this process could only sustain the Sun for around 20 million years. Far short of the 4.6 billion that we now know the Sun needs.

  It took until the twentieth century for a theory to emerge that could cope with the amount of energy that the Sun needs to generate, kick-started by none other than Albert Einstein, who had been keeping busy since his work on the photoelectric effect.

  CANNIBALISTIC SUN: A LITTLE MASS GOES A LONG WAY

  In 1905 Einstein published the famous equation E = mc2. E stands for energy, m for mass, and c for the speed of light in a vacuum.* His incredible insight was that energy and mass were interchangeable. Einstein’s equation shows that even a minuscule amount of mass can be equivalent to an awesome amount of energy, because the equation includes the speed of light, squared. So we have gone from releasing energy from a substance by burning it, whereby 100 grams of coal releases 1 million joules of energy, to Einstein’s saying that, in fact, inherent in the mass of the coal is a much larger quantity of energy. A mass of 100 grams is equivalent to 10 million billion joules of energy in Einstein’s formulation.