On the way of interpreting visual shots, I have some points.
Let's take some of the stock footage of the TOS Enterprise orbiting a planet. You all are aware, aren't you, were such a scene photographed in real life, that the ship would not appear to travel in a curved path, right? What I mean by this is that the ship often looks like it's a model a few feet long that's circling a beach ball a few feet in diameter that's sitting only a few feet away from it. I regard this as a trope intended to help the viewer realize that the ship is circling the planet.
How about this, which TOS shot are you talking about and we can try and re-create it (with the power of computers!
There's a wonderful catalog of every TOS FX shot seen available here:
That way, we can see what the ship appears to be doing at that moment before just saying it should look like any one of these orbits
(or if it's just powering in place because it can.)
Very nice catalogs; thanks for spoon-feeding me both of these pages.
What I said applies to any of these, which includes the iconic planet orbit shots:
The Tressaurian Intersection
- WNM Orbit Towards (Where No Man Has Gone Before - The Enemy Within) 
- Orbit Away (Mudd's Women - Turnabout Intruder) 
- Orbit Towards (Mudd's Women - Turnabout Intruder) 
Exeter fan film has some wonderfully modernized orbit shots that have much better perspective; yet they still seem to be perfectly in the style of TOS. I really suggest checking it out. I have confidence the last part of TTI will be done eventually.