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 preceeding it in orbit.
The sun rising as it does is completely acurate.