It’s literally just a wind that comes from the sun, it’s actually pretty self explanatory. In space, it is not a perfect vacuum, there are particles all over the place. The solar wind is a part of this. The sun sheds plasma and pushes it away at tremendous speeds constantly (because of magnetic fields, radiation pressure, thermal velocities, etc), and this, along with radiation pressure, do in fact push on things. Since the solar wind is a plasma, it’s charged, and thus can be very damaging to sensitive equipment, even apart from the sheer velocity of it.
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