The Sun's Energy

Heat and light	What is the source of the sun's energy? It's a crucial question, because light and heat from the sun are the basis of (almost) all life on earth. Sunlight drives plant life via photosynthesis, and animals survive by eating plants. Almost all microscopic forms of life (bacteria, protozoa, etc.) survive by using the energy of sunlight.
Surface temperature	We know that the sun is a sphere of diameter 1,400,000 km, that its outer regions are hot gases, mostly hydrogen and helium, and that its surface temperature is about 6,000 degrees Celsius (about 11,000 degrees Fahrenheit). Any surface at that temperature will generate heat and light. The burners of an electric stove or a toaster oven, for example, are not at 6,000 C., but when they're turned on they are "red hot"; they emit heat and light and the light is red. If we could raise the temperature to 6,000 C. they would become "white hot", and emit light very much like the sun's. Similarly, a fire is a region of gases at a temperature high enough to generate heat and light. So the question becomes not so much why is there heat and light, but where does the energy come from to keep the surface temperature of the sun at 6,000 degrees?
Fire	To a scientist living in the 18th or 19th century, before electrical appliances, the most likely approach to understanding the sun's energy would be to make the analogy to a fire. When something burns (say, wood, or carbon) there is a chemical reaction between the material and the oxygen in air. Not knowing what the chemicals in the sun are, one could still assume there is some chemical reaction going on that produces heat, and keeps the sun hot. The problem is, how long would it be before the burning chemicals are all used up and the fire goes out, just as logs burning in a fireplace will all turn to ash within a few hours?
The sun's lifetime	It is not difficult to arrive at a rough answer to that question, since we know the sun's mass. The mass is calculated using the law of universal gravitation, and the known orbits of the planets. Assuming the mass is all something like carbon, one can calculate the sun's lifetime to be about 50,000 years. Any chemical burning will lead to a lifetime in that general range.
Inconsistency between age of the sun and age of the earth	But nineteenth century geologists believed that the age of the earth was 100 million years or more. These calculations were approximate, but based on reasonable assumptions about how salt is deposited into the sea, and how marine sediment is deposited onto what are now the continents. (For example, if we assume that all the salt in the oceans got there by being deposited by rivers, and we can measure the current rate of deposition by rivers, we can then calculate the number of years it would take to reach the salt levels found in oceans today.) Since the earth orbits the sun, it is hard to imagine how the earth could be older than the sun. Thus the model of the sun as a chemical fire was not tenable.
Gravitational energy	About 1850, the physicist Hermann von Helmholtz proposed that the source of the sun's energy could be gravitation - that is, the universal gravitational force that every piece of the sun exerts on every other piece. We can see that gravity can produce energy by just thinking of releasing an object, say a baseball, and letting it fall to the ground. Energy of motion (kinetic energy) is produced, as the ball accelerates downward. If we think of the sun as a huge sphere of gases, each atom in the gas feels a net attraction to the center of the sphere, and so all the atoms have a tendency to "fall" in toward the center. As this happens they collide with other atoms, and so their motion is energetic, but randomized. Rapid random motion of atoms in a gas means higher temperatures. Given the known rate at which the sun produces energy, Helmholtz was able to estimate how long the sun, given its mass, could continue producing energy this way. His conclusion was about 20 million years, much longer than the estimate based on chemical burning, and closer to estimates at that time of the earth's age.
Billions of years	Nevertheless, millions of years is not long enough. The best value today for the age of the solar system, the sun and the planets, is 4.6 billion years. We know from radioactive dating that there are rocks which solidified about 4 billion years ago, and that early microorganisms existed close to 3.5 billion years ago. So gravitation cannot be the explanation for where the sun gets its energy.
Nuclear reactions	Things came together finally in the early twentieth century with the discovery of the atomic nucleus (1911), the exploration of nuclear reactions (the 1920s), and Einstein's theory of relativity (1905). In a typical nuclear reaction, several sub-atomic particles come together, interact, and several (possibly different) particles emerge. There are a series of reactions going on in the sun, but the net result is the following combination of particles:

Hydrogen burning	The left side of this reaction shows four protons and four electrons, basically four hydrogen atoms. Hydrogen is the natural starting point, since most of the matter in the sun (and also the stars) is hydrogen gas. Hydrogen is the simplest element, so it's reasonable to expect that in a primitive state much of the universe would be hydrogen. The endpoint is helium, known to be the second most abundant element in the sun. It is often referred to as "hydrogen burning" to helium, and hydrogen is often called "fuel", but one must understand that the reaction is not burning in the sense of a chemical reaction between a fuel, such as coal or wood, and oxygen. It is a nuclear reaction.
Mass converted to energy	Energy is generated when this reaction occurs because the total mass of the particles on the right side is less than that on the left side. It is not just that there are fewer electrons on the right. The most important difference is that the mass of the helium nucleus (⁴₂He) is substantially less than the total mass of the four protons on the left. This is an example of binding energy: The ⁴₂He consists of two protons and two neutrons, but its mass is less than the total mass of two protons and two neutrons. Since the mass on the left side is greater than that on the right, we end up with energy produced when the reaction occurs, energy equal to the mass difference times c². This energy is in two forms: energy of motion of the particles in the sun, and gamma rays.
The proton-proton cycle	Equation (1) is actually the net product of a series of more fundamental reactions. This series is somewhat complicated, so it is discussed in a separate link, which is available for you to read. Content of the link is not a required part of this site. The process of Equ. (1) is called the proton-proton cycle, since it begins with the interaction of two protons. Building up from small nuclei to larger ones is called fusion, and the sequence that takes place in the sun is similar (but not identical) to the fusion reactions being studied as a possible source of electrical energy on earth.
The binding energy of the alpha particle	Why does nature (the sun and the stars) go to so much trouble to make ⁴₂He's? The answer is that among the various small nuclei that are involved in the proton-proton cycle, the ⁴₂He is the most strongly bound. Its binding energy is relatively very large, and that means that if nature creates a ⁴₂He, a large amount of energy is released. Some energy is released in each part of the cycle, but most is released in the last step, where ⁴₂He is created.
Gravitational collapse	The model we have for the origin of the sun is a cloud of hydrogen gas that begins to collapse under its own self-gravitation (as in the thinking of Helmholtz), and begins to get hot. Although this cannot be the mechanism for the sun's generating energy for billions of years, it can be a triggering or ignition mechanism: It initiates the nuclear reactions. (You will remember that nuclear reactions can only occur if the nuclear particles are moving at high speeds.)
A hot plasma	Thus the cloud collapses, and at high temperature the gas becomes a plasma. The hydrogen atoms separate into protons and electrons, and these particles move about randomly. The temperature is hottest in the center of the cloud, and there the protons move so energetically that the reaction in Equ. (4) begins to occur, and the proton-proton cycle starts.
Equilibrium	These processes continue in the center of the cloud, bringing the temperature up to around 10,000,000 degrees. At this temperature the sun reaches an equilibrium, where outward pressure from these "burning" gases balances the gravitational force pulling the matter inward. The energy produced in the center continually works its way outward, keeping the whole sun hot. The outer regions are much cooler than the center, but they are hot enough so that energy is radiated out into space, in the form of the heat and light that bathe the earth.
The sun's lifetime	The sun can stay in this balanced state for a total of about 10 billion years. Given the sun's age as about 4.6 billion years, one can assume we have 5 billion years or so to go. Eventually most of the hydrogen in the center will get used up, and the sun will enter a dying phase.
The stars	The proton-proton cycle powers not only the sun, but most of the stars in the medium to small range of masses. Stars larger than the sun produce energy via a more complicated set of reactions, but the net effect is also that in Equ. (1), hydrogen burning to helium.

KEY CONCEPTS

Age of sun and earth
Sources of the sun's energy
Fire?
Gravitation?
Nuclear?

Hydrogen to helium
Mass to energy
The proton-proton cycle
Gravitational collapse ignites nuclear reactions
The sun's equilibrium