Climbing the Wall
I don't know who first got the idea to picture the Earth's gravity well as this huge funnel, with the Earth at the bottom and the moon and various other satellites as ball bearings rolling or sliding around the top. I'd draw it but you've seen it already in every science museum on the planet. For all I know, Newton may well have had it in his Principia even if they hadn't quite figured out how to make ball bearings at that point.
What's annoying is just how deep the hole in the middle is, and this number I first heard from either Arthur C. Clarke or Gerard O'Neill:
Getting out of the earth's gravity well takes the same amount of energy as climbing a wall 6,000 kilometers high (i.e., if you had to climb the whole way against earth's surface gravity).
O'Neill's point was pretty simple: Why would you ever want to live at the bottom of a hole? Let's build space colonies!
Unfortunately, my point is a little more subtle, so we need some more numbers.
The energy you need just to get to low earth orbit is like climbing the first 3000km, half way out. Even though you've only gained a few hundred kilometers in real altitude, it's a huge accomplishment to go from standing still on the surface to going fast enough to stay in orbit. And it's useful enough to get to a place outside most of the atmosphere, where you have time to think about what you want to do next. But you still have at least another 2000km of wall to climb before you can get anywhere useful…
Like, say, geosynchronous orbit, where most of the communication satellites live — which is already much farther away than people give it credit for. At this point you're a bit more than a tenth of the way to the moon and about 500km from "the top" of the wall, though by that point the funnel has flared out pretty far so that you're actually going 50km outward for every one that you're going "up" (yay inverse square law...). Meaning instead of climbing El Capitan, we're now doing the leisurely stroll from the house to the supermarket — in my case this happens to be a fifty foot elevation gain over half a mile that I'll hopefully still be able to do when I'm 70.
Now as it happens, since our goal is just to get to the moon, we don't need to get all of the way out of the hole. The moon itself isn't all the way out; it's still in orbit around the Earth, see. But it's most of the way out.
Continuing outward from geosynchronous orbit towards the moon, the "wall" continues to flatten out until finally, when you get about 5/6 of the way there, it flattens out completely. You're now just 170km from "the top", in this saddle point where, to either side of you, the wall continues to rise, but in front of you it drops off and you're staring at another big hole with the Moon at the bottom.
Welcome to L1, the first of the Lagrange Points, the five magical places in the Earth-moon neighborhood where moon gravity, earth gravity, and centrifugal force all cancel each other. Put a ball bearing here in exactly the right place and, if it could be undisturbed by perturbations from the sun and the other planets, it would just stay there forever, i.e., orbiting the earth once a month exactly in synch with the moon.
And I really do mean magical, here. Forget Stonehenge, the Bermuda Triangle, or even Disneyland; they've got nothing on L1, as we'll see.
So now we're staring down into this second hole. To be sure, it's not anywhere near as deep, only 450km down to get to the lunar surface, child's play after having come this far. But it's still deep enough to inspire the Lunar Orbit Rendezvous (LOR) people to ask this stupid question:
"Why the hell are we taking everything with us down this 450km hole and back out again?"
Keep in mind that not only do you have to reach the bottom, but you want to be standing still when you get there (so as not to make a fresh crater), which means burning off all of the velocity you accumulate as you fall into the hole.
Which you have to do with rockets because there's no atmosphere.
And then, of course, you have to add all of this velocity back in order to get yourself out of there.
Which gets us to