How large would an orbiting structure have to be to be largely unexplored after 100 years?
For as long as recorded history, the Earth has had two moons - religions were based around the interactions of these two bodies in the heavens, they were worshipped, feared and romanticised.
Then at the birth of astronomy in the 17th century, it was discovered that the smaller of the two bodies was in fact obviously artificial, with hatches, windows, tunnels, structures etc etc.
The first manned space missions in the 1950s and 1960s targeted this structure rather than the moon (which was largely forgotten as a goal) and resulted in multiple countries landing at various points on it.
Assume an accelerated rate of technological advance into space flight, with such technologies such as space planes, NERVA engines, Orion spacecraft et al all being followed through to a usable conclusion, but not more than 5,000 people being put into orbit between the early baby steps of the 1950s until the current date (circa 2050).
Also assume that the structure is not just surface shallow, it is not hollow, nor is it solid but rather its entire volume is a structure, how large would this structure have to be to still be largely unexplored?
Edit: In response to queries for further parameters.
Assume that the structure is largely operational, with human compatible environmental systems, power, lighting, mass transit, gravity etc
Assume that these systems are not necessarily free to use - doors may be locked (eg secure areas, personal accommodations etc), mass transit systems may need a form of interaction not immediately obvious (eg payment), there may be areas of the structure which are exposed to vacuum or irradiated, there may be damage from meteorite strikes.
Assume a political climate similar to our own, on a similar time line - there was a cold war which ended in 1990 for much the same reasons.
Assume motivations both compatible with a cold war, and also a general public desire for information - for example what does the structure mean, who built it, when was it built, what does it mean for us as a species, but equally the desire to retrieve advanced technologies before any opposing country or faction, to achieve the upper hand before someone else does.
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I think you'd need to add a condition - something like once under the surface, remote drones or fast vehicles can't be used (insert reason of your choice) because otherwise you could very rapidly explore using small drones.
So with that out the way you are down to people exploring - and the obvious challenge is getting people there. It is incredibly expensive (in terms of cash, resources and people) to get a tiny number of people to the Moon and back. You aren't going to get an order of magnitude improvement on that by 2050.
So assume only a small, select group of visitors each mission, and missions, even if you throw resource at them, will not be able to happen continuously - you'll run out of resources, or you'll have an incident that while pause space exploration while faults are understood and fixed (see evidence from the Space Shuttle...) and even something a tenth the size of the moon would not be able to be explored fully. Remember volume goes up as the cube of the radius - there's a lot of volume in a sphere.
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