This question will resolve to Yes if either a craft or a person accomplishes what could fairly be called a circumnavigation of another object in the Solar System before January 1st 2075. For example, if a person were to land on an asteroid and walk completely around it, that would resolve to Yes. If a rover were to do the same thing, that would also be Yes. If a balloon/plane/helicopter were to float or fly completely around a planet or moon with an atmosphere, that would also be Yes. Merely orbiting an object would not count. Ambiguous cases like a person walking around a small protuberance on an asteroid instead of the main body would also resolve to No.
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NASA planned to circumnavigate Titan with a balloon, see Titan Saturn System Mission. This makes Titan a prime solar system body candidate for this market.
@severa For avoidance of doubt, can you clarify that above NASA Titan mission would resolve this market YES?
@sesquipedalianThaumaturge A basketball-sized object would be too small. I'm not going to give an exact minimum size, because there might be clever ways of circumnavigating very small objects. Like, crawling around an asteroid the size of a large boulder would count, if you managed to keep from flying off.
@severa Would a very small rover or other robot which crawls around an asteroid smaller than a human be such a clever way?