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Notes -
Ooh, we just talked about this, kinda!
It would be correct to say "hefting its payload, the rocket accelerated to orbit", because the "gain altitude" part and the "gain horizontal speed" part of a launch trajectory aren't two separate parts. A launch vehicle generally starts angling a little bit away from vertical almost immediately as it leaves the pad, and a launch to low orbit usually doesn't reach its final altitude until at or after the point it turns off its engines. There's a slight break earlier, in between the acceleration phases from different rocket stages, but not much of a break and not much change in direction before vs after.
It's mostly just geosynchronous satellites that have a distinct separate "now we're high enough and we start accelerating again horizontally" phase, but even geosynchronous transfer orbits are stable (and faster than low earth orbits, all horizontally, at perigee) so the final phase is called "circularizing" the orbit, not stabilizing it.
Given that I have a million hours in Kerbal Space Program (ESA hire me already!), I already knew all this and then some, but I wanted to keep it as simple as possible while still getting across what a stable orbit even is and how it relates to getting spaceships back down to Earth.
Still, thanks for the added detail!
Thanks for letting me sperg out on the added detail! I suspected you might know it already, but it's surprising how counter-intuitive it is.
As a kid 30-something years ago I wrote an orbital dynamics simulator (in QBasic, with Explicit Euler time stepping, with nothing but circle sizes to indicate z-dimension position and nothing but animation to indicate velocity; I won a science contest award but I cringe to think back on it), and one of the features I added was user-controllable rockets. Keys to control orientation, another for acceleration, others for speeding/slowing/pausing time. I'd ask people to get from a lower circular orbit to a higher one, and basically everybody I asked would try the same strategy: turn the rocket vertical (perpendicular to its current direction of motion), thrust, then turn horizontal again on the theory that that's what they'd need to do after they'd accomplished "up".
To be fair, at the same time I was struggling to understand why porkchop plots all have those gaps in the middle, and I didn't finally get that until long long afterward, when I first had to make an interplanetary plane change in KSP.
I recall being part of a student group at university (Computer Science) that aimed to explore the Apollo Moon Mission's onboard computer. My job was explaining orbital mechanics to everyone...and I completely overshot and took about an hour to do it in a 20-minute time-slot, giving far too much detail.
Somewhat later, I'd write my own (purely keplerian) orbital simulations, mostly in C#.
To some extent, nerds are all the same, no matter the time and place.
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