The TOS Enterprise is not going fast enough to be in a natural orbit.
- How can you make this determination?
- What is the frame of reference of the camera (can't it be in orbit too, albiet a slightly different one)?
- Are you taking into account the apparent rotation of the planet and the length of its day?
The second of three questions is really the most important. The third question is important too, but it doesn't trump everything; since these scenes were not assembled with the aid of a computer, but rather were eyeballed, we know
ahead of time that they won't withstand detailed scrutiny.