How do long range space probes not crash into things?

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How do long range space probes like Voyager 1 anticipate traveling through space for hundreds or thousands of years without hitting something, getting pulled into something’s gravity and crashing, etc?

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Space is generally very empty. Technically yes it is possible that a probe may hit a random object, anything from the size of a grain of sand to the size of a car is small and hard to track, so it’s unpredictable. For larger objects we can generally track them, within the solar system and in the off chance they’re a problem there will be an ever so slight course correction to avoid it. If two orbiting bodies are on a path to intersect, just a tiny change in velocity will ultimately result in them being miles apart by the time they get close to each other.

The Voyager probes were also not really meant to survive this long and go this far. Their current status is pretty much a bonus on top of their completed mission. Space outside the solar system is even emptier than space within the solar system. The chances that the probes hit something is next to none. Eventually they’ll go silent and we don’t really care what happens to them after that, but chances are they will be drifting in space for a long time.

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