Which again leads us full circle to "Why did he install it in the first place?" The theoretical answer is that the Enterprise cannot be operated purely from the bridge unless the rest of the ship is placed under automatic control. If the automation fails, the ship cannot be controlled. You cite "doomsday machine" that the ship CAN be controlled from a single point, which would render the automation center on the Enterprise entirely useless. There's a contradiction there that needs resolving. Either Constellation possesses a capability that Enterprise lacks (and therefore the latter cannot do the same without being configured for it ahead of time) or -- more likely -- the automation center is standard equipment and Decker activated it just prior to beaming down his crew. It is, actually, because the STARBOARD side of the saucer is lit up here while the PORT side is not; that side of the saucer is shaded from the light effects by the bridge dome and the upper levels of the saucer itself. This means the impact point is somewhere on the starboard side of the saucer. For the duration of the explosion and its after effects, yes. Then, as soon as the blast and the secondary effects dissipate, the shadow returns to its original darkness, cast by the impulse deck by the external light source to the ship. Which is exactly what we see. But you cannot see the impact point, which is obscured behind the bridge. If the torpedo was moving down boresight (the camera is in line with the torpedo's flight path) it would be still be impossible, since the torpedo would have to either physically pass through the bridge dome or otherwise "dip" below the visible structure of the dome/saucer to hit that point. Indeed, it could only hit the point you specified if it was traveling (in the camera frame) from roughly top left towards bottom right. From the camera's point of view, the impact point is slightly behind and to the left of the bridge module; IOW, outside of the red lines on the diagram below. Note that the path of the torpedo is from top right to bottom left. At that trajectory it could not have crossed over to the port side of the saucer section before hitting the ship. Actually, that's something they spend most of their time practicing in the simulator. Training ships are used to teach cadets how to live and work aboard an actual ship on a day-to-day basis; transporter operations and away mission scenarios are trained on a situational basis and such training is usually conducted in a simulator or (in the field) in the form of drills and exercises. "Learn how to use the fire control system" is simply not what training ships are used for; "Get used to using the fire control system on an actual ship where you don't have your academy bunk, the bar across the street, the library, your girlfriend or your momma's cooking to keep you comfortable" is. That raises the question of whether or not the Enterprise was actually under Kirk's command prior to the Praxis explosion. If he was, then "under your command" would seem a little redundant, wouldn't it?