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Hopefully by reading this document, you will be able to answer these questions when the topic of solar sails comes up:
A solar sail is a spacecraft with a large, lightweight mirror attached to it that moves by being pushed by light reflecting off of the mirror instead of rockets. Look here for pictures of possible solar sails. The light to push a sail can come from the sun or large lasers we could build. Satellites in orbit around the Earth can survive for many years without any maintenance while using only a little bit of rocket propellant to hold their positions. Solar sails can be made to survive in space for many years as well. But, because solar sails use sunlight that never runs out like rocket propellant, during those years the sail can move around as much as you want it to, such as from Earth to Mars and back, possibly several times if the sail remains in good condition. A similarly equipped rocket would either be ridiculously huge because it has to carry the fuel for each trip, or would need to be refueled regularly.
Before anyone ever took a beam of light and measured how much it could push, there were predictions that light could exert a very gentle push on objects it hits. James Clerk Maxwell developed the laws describing electromagnetism and concluded that light is an electromagnetic wave. Maxwell predicted that when light hits an object and is absorbed or reflected, the light wave pushes on the electrons in the surface of the object, which in turn push on the rest of the object. If the light is reflected, the object gets pushed twice as hard, just as if you would be pushed twice as hard by a rubber ball hitting you as a ball of clay. In 1901-1903, the Americans Nichols and Hull and Russian Lebedev were able to measure light pressure as predicted by Maxwell. Find a physics text on electromagnetism, like Physics, by Halliday, Resnick, and Krane, to see how the force is derived from Maxwell's equations.
When Einstein developed his theories of relativity, and gave us the equation E=mc2, it allowed us to calculate light pressure a lot easier. E=mc2 compares energy, which can be easily measured in light, to mass and movement, which can easily be used to find forces.
If you fiddle around with E=mc2, you find that the force light exerts is the power of the sunlight divided by the speed of light. Like I stated above, you get twice as much force from an object that reflects all the light as you do from an object that absorbs all the light. In order to get this simple formula, force equals power divided by speed of light, the steps taken by Maxwell and others had to be taken first.
Sunlight exerts a very gentle force. The power of sunlight in space at Earth's distance from the sun is between 1.3-1.4 kilowatts per square meter. When you divide 1.4 kilowatts by the speed of light, about 300 million meters per second, the result is very small. A square mirror 1 kilometer on a side would only feel about 9 Newtons or 2 pounds of force. Fortunately, space is very empty and clean compared to Earth, so there is plenty of room for a 1 kilometer wide sail to maneuver, and there is no noticeable friction to interfere with your 9 Newtons of thrust. A sailboat on Earth wouldn't be going anywhere with that little force because of drag from the water and air. Some rockets can push millions of times harder, but the sail keeps pulling so long as light shines on it. Months or years after the rocket runs out of fuel, the sail is still pulling.
Many people assume that because here on Earth they feel wind but not sunlight, that solar sails must be pushed by the solar wind. However, there is a very big difference between space and Earth. Earth is wrapped in a thick layer of gas that is felt as wind whenever it moves. In space, there is no air to move around and cause strong winds like we feel on Earth. The solar wind is an extremely tenuous flow of particles ejected by the sun which exerts very little force on anything it hits. The reason people worry about the solar wind is because many of the particles have an electric charge that can hurt people and electronics, or can push a magnetic sail.