Math, basically.
You can figure out how fast the rocket exhaust will make the rocket go, and what the effects of the pull of gravity will be (I’ll ignore air here). In general things in a gravity well that AREN’T being pushed move in ellipses, orbiting the center of the well … or if they have too much speed, they follow a hyperbola and escape to infinity.
If you know something’s speed and direction, and the strength of the gravity field, you can calculate its orbit; the high point, the low point, the speed it will be going at each, the time it will take to orbit, etc. We use computers for that these days. Kepler, centuries ago, had to work orbital equations out on paper, and he didn’t even have logarithm tables to help! It took approximately forever…
–Dave, ask further if you want to know actually how to find some of the answers
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