Well, here is the first look at Where No Man Orbit Towards.
TOS Enterprise is moving relative to the camera at 357 ft/s. Altitude approx 6,600 miles.
Time of visual shot is ~4 seconds.
So, the questions are:
What kind of orbit could it be? The TOS Enterprise is not going fast enough to be in a natural orbit. Timo's idea of a deliberate powered orbit makes sense. A "standard orbit" might just put the ship over a specific hemisphere of the planet. Loss of power would mean the ship falls out of orbit because she's not going fast enough naturally to have any stable orbit. This jibes with "Return of the Archons", "The Apple" and even "Court Martial" given loss of power equals a very fast drop out of the sky.
It might be a very strange elliptical orbit but we don't have enough visual time to give a good orbital track.
As Timo points out, rarely (if never) is the top of the saucer facing the planet. If they were sensors, it doesn't look like they were meant for planetary survey. If they were skylights, the folks looking through are never treated to a view of the planet they are visiting