Or, how about the "space dive", where they leaped out of a shuttlecraft and suddenly lost all their inertia? How about re-entering the atmosphere in a space-suit without any worries about friction or heat?
Or how about that giant drill? Why did it fall when they cut it off the ship? If the ship was in geosynchronous orbit, then the drill must have been traveling slightly slower than geo-synchronous orbital speed; it should have very gently drifted eastwards.
The Bad Astronomer covered this.
First off, something they got right once I thought about it some. The shuttle left Enterprise to go to the Romulan ship. At first I thought both ships were in orbit, but thatâ(TM)s not true! The Romulan ship had lowered the mining drill from above the atmosphere, but it had to be hovering above the ground to do that, not orbiting the planet, or else they wouldnâ(TM)t be stationary over one spot (true, there is a geosynchronous orbit that keeps you over one spot, but itâ(TM)s tens of thousands of kilometers over the surface, and the ships were clearly just above Vulcanâ(TM)s atmosphere).
So when the trio jump from the shuttle, my first thought was that theyâ(TM)d still be in orbit; to deorbit means theyâ(TM)d need to change their velocity by several km/sec, which is clearly not possible. But they werenâ(TM)t in orbit, so they just fell. OK, +1 internets for the movie.
They would fall fast. And they did! Their speed was a little less than a kilometer per second, which sounds about right. At their altitude there wouldnâ(TM)t be much if any air to slow them, so theyâ(TM)d free fall; as they plunged deeper air resistance would slow them down. At first I thought theyâ(TM)d actually burn like meteors, but in reality (ha! Reality!) they werenâ(TM)t going that fast.