Star Points for March, 1998; by Ray Sterner (guest writer) The Day Star Way back it was thought that the earth was the center of the universe. It looked that way, the earth seems stationary and the sun, moon, and stars seem to rotate around it. Our everyday descriptions are still earth centered --- sunrise, sunset, and so on. And almanacs and astronomy magazines state that on March 20 at 2:55 p.m. Eastern Standard Time the sun crosses the equator and spring begins in the northern hemisphere (and fall in the southern). We now find that the complicated motions of objects in the sky are more easily described by saying that the earth rotates on its axis and orbits around the sun. The rotation axis of the earth is tipped relative to the orbit, giving us seasons as we move around the sun once each year. Over the short term, decades or even centuries, the tipped rotation axis may be thought of as pointing in a fixed direction, currently toward the North Star (the axis actually sweeps out a large circle in the sky in about 26,000 years). The sun crossing the equator may be described in less earth centered terms by saying that as we move around the sun the earth's tipped but "fixed" axis goes from pointing somewhat away from the sun to pointing somewhat toward the sun. It's a lot easier to say the sun crosses the equator so this description will not go out of style. Our days get longer during March, sunrises get earlier, sunsets later. However, our orbit is not quite circular and we actually move away from the sun all during the month, but only by 3/4 of a million miles, not much compared with our average distance of about 93 million miles. We are closest in January and farthest in July, causing about a 7% variation in the sunlight we get during the year just due to the changing distance. The tilted rotation axis is what causes the large seasonal variations. The rate the energy from the sun falls on the earth at its average distance is called the Solar Constant. The value of the Solar Constant is not quite constant, it has been measured by satellites to vary a little. If it varies enough we will fry or freeze, but that's not expected in the near future. Its value is about 1367 watts per square meter, which is 1143 watts per square yard. This applies outside the atmosphere, so every square yard directly facing the sun at the earth's distance has this much power from the sun passing through it. That's quite a bit considering the sun is 93 million miles away. Knowing the Solar Constant, and the sun's distance, we can easily compute the total power output of the sun. If the sun radiates equally in all directions, probably a good assumption, then the power falling on each square yard of an imaginary sun centered sphere with a radius equal to the earth-sun distance can be added up. The answer is 384.4 septillion watts. That's 3844 followed by 23 zeroes (in computer notation 3.844E26). The earth intercepts only a very tiny fraction of this total, and even part of that gets reflected right back into space before it can do much for us. The other planets and objects in orbit about the sun intercept a tiny bit of the rest, but most of the sun's energy heads off into deep space; some of it may be viewed by beings around distance stars. Where does the sun get its energy? Astronomers are now quite sure it is by nuclear fusion, the same basic mechanism as used by hydrogen bombs. Hydrogen is a large fraction of the sun's mass. If four hydrogen nuclei are squeezed together the resulting helium nucleus weighs just a tiny bit less than the original hydrogen nuclei together, there is a small mass difference of about 0.7%. Einstein's most famous equation, E = m c squared, gives the relation between mass and energy. E stands for energy, m for mass, and c is the speed of light. The speed of light is a big number, about 186,000 miles per second, which must then be squared. It is thought that the sun combines hydrogen into helium, indirectly, and the mass difference is given off as energy. We know the sun's total energy output, and we know the speed of light, so using Einstein's equation we can compute the equivalent mass. I won't bore you with the details, but the final answer is that about 4 million tons of mass is converted into energy every second. This is just the mass difference between the hydrogen and helium nuclei, so a total of 564 million tons of hydrogen are converted to 560 million tons of helium every second. Don't worry, the hydrogen in your drinking water won't suddenly fuse into helium, it takes extreme conditions, such as the center of the sun, where the temperature is tens of millions of degrees and the pressure is so great that the hot gas is seven times denser than lead. The inside of the sun is so hot that a National Geographic article some years ago showed a cross section of it to be black inside because most of the radiation at those temperatures is in the invisible x-ray wavelengths. Their diagram was wrong, even though the maximum energy is given off in invisible wavelengths the visible light would still be thousands of times brighter than the surface. The sun's super bright core, where 4 million tons of mass are converted into energy each second, is well hidden from our view, fortunately for us. But it's something to think about next time you watch a sunset.