When unmanned spacecraft accelerate in space, what causes them to slow down?
The speeds of spacecraft are affected most strongly by the gravity of the planets and the Sun. For example, if you want to send a spacecraft from Earth to Jupiter, you first have to get it away from the Earth. If you just shoot it into space, the farther it gets from Earth, the slower it will go. If you don't start it out fast enough, it will eventually slow down to zero velocity, and then fall back toward the Earth, just like if you throw a ball into the air-- you can't throw it high enough to escape the Earth, so it falls back toward you. But if it has escape velocity it will never fall back.
Once the spacecraft is free of the Earth's gravity, you have to give it enough speed to get it out to Jupiter. As it moves away from the Sun, the spacecraft will slow down. If it doesn't have enough velocity, or enough rocket fuel to increase its velocity, it will never get all the way out to Jupiter.
Spacecraft in special situations can also be slowed down (or sped up or turned) by other effects, such as light pressure from the Sun, by drag from an atmosphere if they're close to a planet.
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