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When scientists are planning missions, they sometimes have to take into account the fact that the light from the Sun pushes on the spacecraft. But with solar sails, they can also use that pressure to propel the craft along.

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Sources:
http://descanso.jpl.nasa.gov/evolution/AAS_08-051.pdf
http://time.com/3643896/kepler-planets-repair/
http://www.planetary.org/blogs/jason-davis/2014/lightsail-update-launch.html
http://sail.planetary.org/
http://www.jpl.nasa.gov/cubesat/missions/neascout.php
http://www.lpi.usra.edu/sbag/meetings/jul2014/presentations/0930_Thu_Castillo_NEAScout.pdf
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In 2010 the Japanese Ikaros spacecraft became the first probe to successfully propel itself through space using nothing more than light from the Sun. That's because it had a Solar Sail which is just like a regular sail, except that it uses light to push itself along, instead of wind. Ikaros is still out there, orbiting the sun, but back here on Earth, scientists are preparing for new missions with solar sails. Even though we didn't really start using them until a few years ago, most of the physics behind solar sails were worked out in the early decades of the 20th century. That's when physicists who studied relativity and quantum mechanics like Albert Einstein, Max Planck, and Louis De Broglie showed that photons that make up light have some weird properties.

It might help to think of photons like little massless, sizeless tennis balls, that are also waves at the same time, because photons act as both particles and waves. Okay so photons aren't really like tennis balls. But they kind of work in similar ways when it comes to momentum. When a tennis ball hits something like a chain link fence, it transfers momentum to the fence. Which pushes the fence in the direction the ball was moving. Then the posts pull the fence back, which is why it rattles and swings back and forth.

Light pushes solar sails in pretty much the same way, but there are no posts to keep them in place. Light hits the sail, some of the momentum is transferred, and the sail is pushed in the direction the light was moving. There is one big difference, though, photons don't have mass, and tennis balls do. And and object's momentum is usually defined as its mass multiplied by its velocity. Since 0 times anything is still 0, massless photons seem like they shouldn't have any momentum to transfer. 

Those physicists in the early 20th century, though, showed that photons manage to have momentum without any mass. Instead, a photon's momentum is proportional to its frequency, how quickly it oscillates back and forth as a wave, instead of to its mass. That means that different colors of light have different amounts of momentum. Blue light has a higher frequency than red light, so photons of blue light have more momentum than photons of red light. And would push a solar sail more.

When light pushes it's called radiation pressure, and it's something that space scientists have been using and accounting for since the early 1960's. Like when they were designing the Mariner 4 Mars probe, for example. Which used radiation pressure to stabilize itself and make sure it stayed on course. Because they compensated for the push from sunlight, Mariner 4 became the first probe to ever return pictures of another planet from deep space, when it sent back images of Mars in 1967. 

Radiation pressure is also being used to keep the Kepler space telescope stable. We've talked about Kepler before, its main mission was to find planets around other stars by staring at them for years at a time. To do this while orbiting our sun, Kepler needed to be able to rotate slightly, every once in a while, so it could keep an eye on the same patch of sky while it moved. But in the vacuum of space, friction won't stop you from rotating once you've started, so Kepler had what are called "reaction wheels", which would basically spin in the opposite direction to stop the telescope from rotating out of control.

In 2013, when two of these reaction wheels stopped working though, it looked like Kepler's days were numbered, but in 2014, the team working on the project was able to use the sun's radiation pressure to change where the telescope was facing. And it's still working more than a year after the fix, all thanks to light's ability to push.

It's one thing to keep a ship stable, but for radiation pressure to be a practical way of propelling a spacecraft, solar sails have to be huge. Like tens or hundreds of square meters, because there needs to be room for a lot of photons to hit it. To give you an idea of how small a photon's momentum really is, it takes about 2 million billion trillion blue photons to match the momentum of a single, well served, tennis ball. But, following the example of Ikaros, some of the missions planned for the next few years are going to use solar sails. 

The Planetary Society, a group whose founders include Carl Sagan, and whose current CEO is Bill Nye, is planning a mission for 2016, they call LightSail-1, which will orbit around earth with a solar sail big and reflective enough to be seen from the ground. And NASA's near-earth asteroid scout mission, slated for July 2018, is going to test out a solar sail on its way to scope out near-earth asteroids. Both of these missions are going to be unmanned, but there's no reason why solar sails can't be used on missions with humans on them someday, moving through space using only the pushing power of light itself.

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