We already have quite a lot of speed from the earth’s rotation, you can use that to help you go fast, easier, by accelerating in the same direction you were already going, which is parallel to the Earth’s surface.
Then the moon is also already moving, so if you can find a time when just speeding up a bit (a lot) from the direction you were already going will get you in front of the moon, that saves a lot of effort.
Now when you get to the moon, you’re going too fast and will crash, so you want to slow down safely. It’s easier to do that in a controlled way when orbiting the moon, because if you don’t slow down enough you won’t become moon dust, and if you slow down too much you won’t miss. Once you’re in orbit you have much more control and leeway to choose where to land and how quickly.
All of this works on the way home too, but then you’ve got earth’s atmosphere to deal with. As it gets thicker it slows you down, so by coming in at a shallow angle you can use the air to slow yourself down rather than heavy fuel.
Every pound of extra fuel you bring makes the whole rocket heavier and harder to lift (which then needs more fuel), so the less fuel they can bring, the better.
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