Orbital Mechanic Basics & Orbit Planet

 I had an [oh my god humans are so dumb] moment, so now anyone who doesn't already know orbital mechanics gets to learn the basics.

 

 It's this: to get to a higher orbit, go faster. To get to a lower orbit, go slower.
 In particular, you usually have to do it twice. Doing a burn affects the altitude of your orbit on the far side of the primary. Thus, when you get to your new aphelion, you need to do another burn, to even it out. Alt: you can do an even(ish) burn through a whole orbit, although this is plain stupid if you're using newtonian mass-ejection rockets. 

 Humans naively think that getting to a higher orbit means pushing yourself up. Hey. Morons. What happens when you push yourself up sub-orbitally? You come back down. Guess what happens in orbit? You come back down. Retards. Pushing yourself up is not useful unless you have a ledge up there to hang onto, to prevent the fall. No ledges in space.
 In space there's no ground to hit, so you go up again. And down. And up. Pushing yourself up (or down) while in orbit simply adds an oscillation to your orbit.
 Conservation of energy means going higher means going slower. Your altitude drops, as per the first principle of orbit. Going lower means going faster. Altitude rises. So on forever. Pushing up or down is a nearly completely useless way to spend energy.

 Something something saturn rockets? They see you get into orbit by pushing up. But you don't. If the rocket went straight up, it would also come straight back down.
 In addition to the dumb, there are lies. Escape velocity isn't a real thing. If there were only one large mass in the universe, everything would be its satellite, the only question is how distant the aphelion was. Provided gravity is continuous and doesn't cut out at some distance...it doesn't matter how fast you're going, at any finite velocity, you will decelerate infinitely. You reach zero velocity and come back. In the real world you can make smaller masses (earth) negligible compared to bigger masses (sun, galaxy) but you never literally [escape]. 

 

 On the other hand, perpendicular forces seem fairly intuitive. It changes only the direction of your orbit. You're making a great circle, and now you're making a different great circle through the same place you turned. 

 A truly counterintuitive thing: higher velocities have higher linear velocities, but lower angular velocities. The orbit takes longer. 

 Imagine a planet spinning so fast that at the tropics, the surface is moving at orbital velocity. Probably it's impossible, and if it were possible, it's likely not possible to have an atmosphere on this planet, but it would be a wild place. If you kick up a rock, it would get into orbit. Levitate. Then smack into you, as your feet are anchoring you to a higher angular velocity layer.
 Regardless of how heavy the planet is, you would be weightless. It wouldn't need to push up on you to keep you from sinking into the ground. Your feet wouldn't in fact anchor you without magnets or claws, you would lift off and the ground would slide under you toward sunrise, as you orbited at the proper orbit for your centre of mass.

 What would happen as you move toward the equator? Coriolis sand seas? Orbiting gravel constantly jostling against relatively-faster moving lower orbits?
 This thought experiment is not some exotic thing I can specially do. Physicists are just boring. Alchemists had style, and were therefore better. 

 Fast bullets are around 4000 kph. Orbital velocity on the moon is around 6000 kph. Due to lack of air, you can have ankle-height orbits if you want. Though you have to take into account the fact the moon isn't a sphere. The ankle-height orbits aren't stable due to mountains implying nonlinearities.
 Artillery on the moon can hit any other point on the moon.