It is unreasonable on many points. First, the ship would not be merely orbiting the station, they are both too close in mass for that. The ship and the station would be orbiting each other in a sort of cosmic dosee-doe. This is a much more difficult thing to be effected by a single ship applying a little thrust. Its very presence affects the station. It's not as easy as a tiny object going into orbit around a much more massive one.
Why not? Countless natural objects orbit each other that way without needing any kind of thrust at all -- Pluto and Charon, for instance, or the binary asteroid
90 Antiope. Once established, it's a stable relationship.
But a station like K-7 doesn't usually have only one ship calling at a time. How do you calculate these orbits when there are two, three or four ships acting on the station at once. Suddenly we have an enormously complex and variable dance. And they all have to have non-intersecting orbits. Suddenly, much of the station's habitat would have to be occupied by traffic controllers, constantly monitoring the swarm of bees buzzing around them, pulling them and each other off course each time they got closer to each other.
No, what you propose is preposterous. There is no reason for it. Any number of ships can float in the general vicinity of the station. Each ship responsible for keeping its own relative position with minor and infrequent corrections.
The very fact that you use the word "float" shows the fundamental conceptual flaw in your argument. To float is to hover as if weightless. But as I've been saying, gravity isn't optional. The ships and the station cannot simply "float" at a constant separation forever. They have mass, they are in an essentially frictionless vacuum, and therefore they
will attract one another gravitationally, no matter what. That's fundamental to the physics of the situation. The only thing different between your proposal and mine is in how the ships' operators choose to cope with that gravitational influence. If the ships are keeping station by thrusters as in your scenario, they'll still have to calculate thrust to cancel out their mutual gravity (assuming they stay on station for several days, long enough for it to affect their trajectories by more than a few millimeters either way). So it's still going to be "enormously complex and variable" if they do it your way.
But you know what? There are indeed ways that three or more bodies can orbit together in a stable or semi-stable fashion. Surely you're familiar with
Lagrangian points. Once you have the
Enterprise in orbit of K-7, you could put the Klingon ship at the L-4 or L-5 point. Or maybe L-3, which is diametrically opposite, albeit only semi-stable. Of course, since the ships are close to each other in mass, the standard Lagrangian-point physics wouldn't quite apply, since they assume the two main bodies are far more massive than the others. But the basic principle is sound. And there are plenty of other
stable three-body orbital configurations.
Of course, I'm not saying they
have to rely on orbit in every instance. Obviously it's not the only possibility, since they
do have thrusters. I'm just saying it
could work in certain specific cases. If there are a lot of ships flitting around, then it might be difficult to maintain a stable orbit -- although over the course of a few days, it wouldn't make much difference, since again we're talking about an orbital period on the order of one month. But in a two-body problem like the specific one we've been talking about, there's no reason it wouldn't work.
I would generally agree with this. But I don't throw the baby out with the bath water. In the case of this particular instance, there is a conflict between the various scenes. Something has to give.
Nothing "has to" give. This is storytelling, the use of created images and words to convey the illusion of an event. All we have to do is not take the illusions too literally. If two images contradict each other, we can choose one or the other, or we can treat them both as imperfect representations. I try to look past the surface images and imagine the underlying idea that they're approximating.