If you cut the engines, while the Enterprise is hovering at 200 miles, she would hit the ground in 4 minutes and 16 seconds. From maximum transporter range of 16,000 miles, she would hit the ground after a leisurely 38 minutes and 11 seconds. Both times assume no atmosphere, I'm afraid I can't quite figure that out.

Twice the distance (in meters) divided by 9.81, the square root is your time in seconds.

The Captain's Log in

*Naked Time* said they had nineteen minutes left. But that was a while after Riley cut the engines.

There might be occasions when they're mapping a world where the ship would be in orbit.