Star Trek should have nuances to that, too. Tidal forces would be trivial for a starship that has propulsive power to burn - no need to spare the gyro wheels or the RCS fuel. And nobody inside would feel the forces, not even the all-important Perfect Balance Laboratory, because artificial gravity.
On the other hand, starships probably would not want to be in freefall. After all, they don't have to - they can supposedly maintain 1G acceleration for years at an end if need be. And most of the time, they don't approach a planet in order to study the planet - they approach it to study or otherwise exploit a specific point on it. They'd very much want to orbit only above that point, then, rather than inconveniently going behind the planet every now and then. Say, transporters are line-of-sight devices, incapable of penetrating more than a couple of kilometers of normal bedrock, so going below the horizon would be a baaaad idea.
An orbit for a starship would be what an orbit is for an aircraft today, then: a figure eight above the point of interest. Which is what the maneuvers of starships typically look like, too, with incredibly tight oncamera turns where even the tightest freefall orbit should show no turning whatsoever. Who knows, perhaps the sideways posture of ships in orbit is due to them constantly banking into the curve, for whatever the reason of starships always banking into the curve.
I trust we'll see the DIS ships doing banking a lot, too, although orbital shots of late have been more varied in orientation and less likely to show tight turns. Are we going to see the windows used for something specifically window-functional, or merely as wide-angle viewscreens? I doubt planets and orbits will feature into that much. But spacewalks and uncomfortably proximal Klingon space sarcophagi just might.
Timo Saloniemi
Until there's an urgent saucer separation and you try a saucer landing… with your bridge on the underside of the saucer… 
