It’s seems so impossibly hard to me, given that at those distances being just a single degree too far to the left etc. would result in missing a distant planet completely.
In: Planetary Science
The short answer is it’s all math. The locations of the planets are known to high precision and the location of the probes can also be measured.
Space probes always have small course correction burns planned to fix up the trajectories along the way.
They begin with the fact that while on the ground the rocket is already in orbit around the sun. As others have said all of the the rest is a whole lot of math.
To get to Mars you modify the existing orbit around the Sun to get into an orbit around Mars.
Lots smart people doing some pretty hard math and the space probes have a little fuel reserved for corrections for unforeseen effects that happen allong the way. Though those corrections realy have to be small if they make a big error in the calculations the space probe is just “lost”. They wont lose connection but they wont get to their target.
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