For a spacecraft going outside of Earth orbit, most of the navigation happens at launch and very early on, with only minor corrections later on. The problem you run into is that every kilogram of stuff you want to put into space is really expensive and requires a lot of fuel, so if you’re trying to put a whole propulsion system *and* fuel for it you need a way bigger rocket to launch it all. The Apollo missions had this challenge, and while it’s feasible it’s something you’d rather avoid.
So how do you navigate at launch? Well, the great news is that planets, asteroids, moons, the sun, etc. all move very predictably, so we can model a route that our spacecraft will take for the next 5, 10, 20, 30 years all before even launching it. At that point, we wait for the launch window when we’ll be starting on that route, send the rocket up, and effectively just chuck the craft into space along that route. After that point, we let gravity do all the work for us. Minor course corrections might be done due to impacts with small things or momentum imparted from solar storms, the force resulting from reangling instruments, etc, and those can be done with small boosters we put on the craft along with what fuel we do send up. Those minor corrections can have really big impacts when you’re talking about traveling millions of miles over years of service, but for the most part once the thing is disengaged from the boosters and the payload is traveling freely, the bulk of the navigation is done.
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