RSG: Ship Control
Both "manual" and "scripted" options allow for a full variety of gameplay, with manual flight mode used for battles and for players that prefer a more hands-on approach.
Manual Flight Mode
Controls allow for full heading, pitch, roll?, and lift/strafe control.
Scripted Flight Mode
For scripting details, see the Scripting section.
For people in the 24th century, computers are the easiest way to go about precise piloting. Sample programs like "Geo-synchronis orbit", "Plot a course", and a mining program to give sample code for combat scripting.
For players with multiple ships, scripts for wingmen, search parties, or escorts could be made.
Basic Newtonian laws, of course without too much friction.
Perhaps in proximity with a very large asteroid, moon, or planet, gravity should effect the trajectory in manual mode.
With blobs of interesting stuff continually moving around - it'll be necessary to grab the orbital parameters of any bodies you're interested in so that you can find them again. As in the real world, the longer you observe a body and the more times you rediscover it in different locations, the more accurately you know where it'll be at any given time in the future. This should be reflected in the way the navigation system works.