I'm having trouble understanding your problem with the original statement. To me, it clearly means that with the facilities available (no enormous rockets, for example) it can't easily start from the Earth's surface and get into orbit.
Approaching the Earth is a completely different issue, and I don't understand why you mention it. It simply isn't a problem if you're already in space because you make sure you go into some sort of orbit (elliptical, parabolic or hyperbolic - any will do). You easily have enough speed to do this because you're falling into the gravitational well, and you simply need to deflect your path to one side, miss the atmosphere, and you're on a hyperbolic orbit. Slow a little and you're in a large elliptical orbit. Slingshot properly around the Lagrange points (including "bouncing off" the unstable ones) and you can convert to a "standard orbit" with very little effort.
Launching from the Earth's surface requires a huge amount of energy, and it's been stated that it wasn't done.
The statement that it wasn't done apparently applies to a different canon; there's apparently quite a lot that's changed in this one. However, the amount of energy is trivial compared to what starships in the Trek universe must be capable of. Impulse engines are supposed to be able to drive the ship to some respectable fraction of the speed of light, so no matter how they work, they should be able to get the ship off the surface of the Earth. I think the fact that the Trek universe has artificial gravity solves all of the handwavy problems, though, even apart from that, so there's no canonical technical problem here.
"Launching from the Earth's surface requires a huge amount of energy, and it's been stated that it wasn't done."
This appears to be the key to the nerd rage. If Starfleet didn't build the craft on Earth then showing them in the new movie being built on Earth is a mistake. But it's not a question of physics.
Yes, I agree completely. The first part of my post was expressing why I found the question about approaching Earth misguided, irrelevant, or inappropriate. Clearly the Nerd Rage is just about the inconsistency with the "earlier" episodes.
The comments about the physics also sparked a conversation about escape velocity here in the office. It's easy to compute that orbital velocity at grazing altitude is about 8 km/s. People confuse that with escape velocity, which is sqrt(2) faster, or about 11.3 km/s.
The real confusion arises in that a craft never needs to reach escape velocity to escape. You can happily escape without ever travelling faster than 6km/hr - walking pace.
If this confuses you, it's fun to work out why. And how. And why NASA doesn't do that. The sums are fairly easy, it's the conceptualisation that's hard.
Approaching the Earth is a completely different issue, and I don't understand why you mention it. It simply isn't a problem if you're already in space because you make sure you go into some sort of orbit (elliptical, parabolic or hyperbolic - any will do). You easily have enough speed to do this because you're falling into the gravitational well, and you simply need to deflect your path to one side, miss the atmosphere, and you're on a hyperbolic orbit. Slow a little and you're in a large elliptical orbit. Slingshot properly around the Lagrange points (including "bouncing off" the unstable ones) and you can convert to a "standard orbit" with very little effort.
Launching from the Earth's surface requires a huge amount of energy, and it's been stated that it wasn't done.
Now, what was your question?