Franz Joseph's telescope brings forth a question about the field of view of a starship's sensors.
The FJ contraption seemed to be on a pedestal of some sort that would perhaps allow it to be extended and pointed at targets without pivoting the entire ship; otherwise, the sensor would only stare aft, which may not be particularly practical. But what is practical for a starship? There's the big forward-pointing dish, but then there are the supposed sensor domes at top and bottom - and none
of these devices actually face the planet the starship is orbiting when Spock performs sensor studies on surface phenomena. (Nor does the FJ telescope, for that matter.)
In TNG, there are frequent references to "lateral" sensors, especially in the context of studying specific point targets (rather than in the more intuitive context of listening to what's happening all around the ship and trying to pinpoint a source). Does this perhaps tie in to Kirk's habit of turning one cheek or the other of the ship towards the planet of interest?
Is it a case of something, perhaps warp drive, creating a huge blind spot in front of a starship, so that the only sensors worth having must be lateral, or even aft-looking?
FWIW, there's "The Corbomite Maneuver" where our heroes seem to be doing exactly what Zap
proposed: taking star photos from another angle far off Earth, yielding stereo-view benefits and the ability to peek past obstructions. We don't learn what instrument achieves this, and whether it's the instrument being pointed or the ship, but it still appears that photographing starscapes is worth doing in the 23rd century.