Hober Mallow wrote:
... the Enterprise is actually orbiting Earth backwards.
That's the most likely answer.
The Enterprise in it's "dry dock" was above the city of San Fransisco, you could make out geographic features on the ground. The Enterprise's starboard side was facing the ground and the dorsal direction was north.
At theis point the ship is in fact orbiting backwards.
Given the apparent size of the Earth, the ship, dry dock and space station are not in geo orbit.
When the ship left dry dock it actually did so by slowing it orbital speed, but was still moving ass end first. The dry dock now fpreceeding it in orbit.
The sun rising as it does is completely acurate.
Whether the enterprise is moving ass end first in relation to the earth as it departs space dock depends on whether the dock and the ship is in a prograde or retrograde orbit. If the dock was in a prograde orbit, then the scene is plausible as the camera and the ship is racing eastwards and outrunning the earth's day-night terminator line, and is in effect hurrying into the sun rise, the only point being the ship is racing backwards towards the terminator slightly slower than the camera and so appears to be moving slowly forwards towards the camera.
If everything had been in a retrograde orbit,ie moving west, then enterprise is indeed racing front end first. In this case the scene is impossible as enterprise must be below geosynchronous orbit and running west at a higher speed than the day night terminator.