My favorite way to describe orbits is 'constantly throwing yourself at the ground but moving so fast that you just keep missing', hence the constant free-fall/zero-g.
How fast do you have to go? Easy. Look out at the horizon far enough that you can see it drop (for example a mountain etc). You have to go so fast that in the time it takes you to reach that point, you only drop by the amount the horizon falls.
Could you make a cruise missile that didn't need any wings or other surfaces for lift - only forward propulsion - that just went so fast that it was effectively in orbit, but nor far above the ground?
You can't stay in orbit with plane wings because of air resistance, and with so little air you need rocket propulsion (for now, at least). But that's not to say there aren't some interesting games to be played with wings on the way up.
> This leads us to the central problem of getting into orbit: Reaching orbital speed takes much more fuel than reaching orbital height. Getting a ship up to 8 km/s takes a lot of booster rockets. Reaching orbital speed is hard enough; reaching to orbital speed while carrying enough fuel to slow back down would be completely impractical.[5]
Did SpaceX just solve this problem and rendered this paragraph obsolete? Or is that Falcon 9 reached space and turned around without achieving orbital velocity?
That paragraph was in reference to zeroing out your velocity before re-entry. The Falcon 9, iiuc, uses a combination of thrust and aerodynamic forces to slow itself down / put itself on the correct trajectory.
It's also worth noting that they only land the first stage, there's an entire next stage which isn't reusable which adds further speed to achieve full orbital velocity.
"The reason it's hard to get to orbit isn't that space is high up. It's hard to get to orbit because you have to go so fast."