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Is there anyway to convert energy to motion IN SPACE? Let's say a satellite collects electric energy from sun using solar panel. Is it possible to convert it to Linear motion? The only way I know to change linear motion in space is by throwing stuff out (Ions, burned propellants etc).

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Yes, light has momentum, so you could use your collected electrical energy to create a beam of light to propel the satellite. However, you need to bear two points in mind- firstly, the recoil from the beam would be tiny compared with the energy taken to produce it, and secondly the collection of light from a solar panel would involve the transfer of momentum from sunlight to the satellite, so you would be propelled away from the Sun in any event.

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Conservation of momentum implies that you can only use reactive acceleration. However if there are planets moving around you can use gravity assist.

The now ongoing ESA Bepi Colombo mission to the planet Mercury uses this method extensively to decelerate its fall towards the Sun.

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There is such a thing as a Photon Rocket or Photon Drive. This takes advantage of the fact that photons have momentum. However, you are not going to get a lot of thrust out of one.

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The most direct method is to use the Earth's magnetic field.

It is generally used only for attitude control (i.e. generating angular momentum), but nothing (except the low efficiency, of course) stops you from using if for generating linear momentum as well.

Think about Earth as a big stator magnet and your satellite as a rotor with a coil.

(it is still throwing stuff away, in this case the "stuff" is the Earth, but it is not throwing stuff that you have to carry with you)

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You should read up on solar sails, electric sails, and magnetic sails if you are interested in propulsion near stars. A solar sail uses the momentum of solar photons to drive a ship, while electric and magnetic sails use the momentum of the solar wind (charged particles) to do the same.

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You're right, the only way to change linear motion in space is by throwing stuff out, and why is that a problem?

Instead consider, most obviously, a nuclear submarine which any number of people think somehow moves directly on nuclear energy. Really?

It would be just as accurate to brand the critter a "steam submarine" or by the same token to rename the earlier railway "steam" trains as "coal" or "wood" engines.

Either actually turns its energy into power through steam boilers, whether the boilers happen to source their heat energy from nuclear reactors or coal or wood fires.

In principle, yes, your craft uses solar energy to generate electricity, uses that to boil water then exhausts steam to create motive force.

No few writers pay lip-service to that principle by referring to "reaction mass" but how is that more useful than referring to nuclear or solar energy in the first place?

Please remember, none of that says anything about efficiency or sustainability.

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