Engineering Hull underside
The
yellow circle is definitely an enigma but also the perfect ‘excuse’ to wrap a circular ship’s corridor around it (suggested by various scenes in TOS that take place in the engineering hull). Ironically, I had never thought of this until I noticed the circular computer core in the engineering hull on the three-dimensional cutaway poster of the Enterprise-D where the artist was possibly looking for and eventually creating this kind of ‘excuse’.
Back in the 80’s I did a cutaway blueprint of the TOS Enterprise and assumed that the yellow circle should be the bottom part of a probe (launching) cylinder. After all, there needed to be an egress possibility for the flight recorder in “The Corbomite Maneuver”, the satellites in “Operation Annihilate” and the probes in “The Immunity Syndrome”. A 360° rotating cylinder would provide optimal flexibility to launch flight recorders, satellites and probes in almost any direction you wanted without changing the ship’s trajectory.
And unless you needed to launch sensory equipment as a probe, that same sensory equipment could be used during normal astrophysical examinations. Just turn the cylinder with the corresponding probe towards the stellar object you want to examine. Done with optical astronomy? Turn the cylinder a few degrees to do infrared, next. After that an examination of radio, ray, and neutrino astronomy by the little rotation of the cylinder in the shortest amount of time. I presume Stellar Cartography (“The Changeling”) aka Auxilary Control Room to be located somewhere above this cylinder (while I naturally enjoyed my theory being supported location-wise by TOS-R I disliked its “bomb bay door” concept. But then again, I’m probably biased

).
Peter Chung did a schematic to visualize / emphasize the exterior locations of the engineering hull underside markings but accidentally also illustrated how such a probe cylinder could look like when extended:
http://www.trekbbs.com/showthread.php?t=119751&page=12