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
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.
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