For “largest”, do you want just one dimension (i.e., greatest length), or three (greatest volume)? I’d expect the longest object ever moved a practical distance by humans, for purposes of moving that object, would be a train.
As soon as someone mentioned gravity assist, we’ve been in the regime of “some kind of effect, even if inappreciable.” Anyway, the Ulysses flyby of Jupiter was at a distance of 6.3 Jovian radii. Parker Solar Probe has gone to within 35 solar radii of the Sun already, and will eventually get to 6.9 solar radii.
I could also point out that I once pointed a flashlight at the Sun, which means I moved the Sun via photon pressure.
How about an aerial tramway (or ropeway)? That’s basically a series of gondolas hanging from a cable. The whole cable moves - 96km of it in this case.
:eek::eek:
Leo Bloom, for the love of god, please limit the definition of moved to mean “more than 12 inches”. 
I think we’ve left “fair” off OP+1…
Which is just fine.
Also cool.
More to the initial idea, of movement not already localized: the line/wire of a wire guided missile can unspool some 4 km.
If gravity can smoothly trail off to an infinitely small value no matter how far away you go, rather than going under some sort of resolution minimum and zeroing out completely at some point, then all matter within range of Earth to have experienced any gravitational effects since the “first” human, would be in the running.
The first human made some choice between going left or going right. That choice changed the gravitational pull that her own mass had on the rest of the universe. That choice has been radiating out at C since that moment, minimally changing the trajectory of everything within 2 million to 300,000 light years, depending on what you consider the start of humanity.
A debatable answer for longest: The first cables laid down for trans-oceanic communications. Those are thousands of kilometers, and all of the cable had to move to be put into place… but it wasn’t all moving at once, and the parts which were moving were mostly the parts that were still on the relatively compact spool.
For a cable that moved all at once, how about the tether from STS-75? STS-75 - Wikipedia They got almost 20 km of line out before the tether melted.
Per this reference, the world’s longest, single-belt conveyor belt is about 11 miles long, and is in both India and Bangladesh. https://www.mcshanemetalproducts.com/blog-post/conveyor-belt-world-record-holders/ (Cue airplane jokes.)
If icebergs count, what about rivers? Build a dam somewhere, and suddenly you’re moving decades of accumulated rainfall. The Chinese built a diversion 700 miles long, moving 45 billion cubic meters of water a year, about equal to 1% of the Mississippi’s flow every year.
And then I guess you can start thinking about climate change and water transpiration altered by greenhouse gas emissions. Unintentional geoengineering accidentally moving deserts, I suppose.
Since you bring up dams, the water behind them has changed the rotation of the Earth. Do astronomical answers count if they have been measured? No one’s measured the changes to Jupiter’s and the Sun’s movements that are due to humans, but they have this one.
If you really want to cheat the premise but be technically correct, the first time a human moved has affected the movement of all mass within a sphere with radius c * (time between then and now).
And even without getting into astrological phenomena, so much of this depends on where you set the boundaries of an individual “thing”. Is an interstate road network a “thing”? 4 million miles of roads took a lot of moving of parts to create one massive, interconnected “object”. Even Route 66 by itself is massive.
Likewise, the component electronics and cables that make up the Internet could be a “thing” – it’s all one thing, not entirely dissimilar from the circulatory system of an animal, and took very deliberate human effort to create. The electrons it pushes around, though, measure a measly 50 grams or so.
Do geological phenomena count? Fracking causes earthquakes, literally “moving” the earth… not a lot, but possibly more than the “12 inches” test above. We’re likewise moving the global jet stream via global warming. What about the Panama Canal, moving entire oceans?
The Panama Canal does not move any ocean. Not even a little bit.
I submit that seismic shock waves traveling through or around the earth constitute a movement. Therefore, any nuclear device strong enough to transmit shockwaves detectable on the other side would be it.
The Great Pyramid of Giza has an estimated mass of 5.9 million metric tonnes. While do doubt not all of its pieces were moving at once one could speculate that quite a few pieces were being shipped, moved on site and put into place at once.
The max. mass being moved at once might be the record for most massive amount being moved by man in one project in a literal sense. Without aid of motors, rockets, explosives, etc.
Nosing around I see various guesses including about 90 tonnes of stone being put in place per hour. Maybe something on the scale of 1000 tonnes in motion at once? But that seems high even with a low estimate of 10 years to build.
In that case we could say the Milky Way galaxy or even the local group.
Before I read through this thread, I thought the Chernobyl New Safe Confinement would be a contender at 31,000 tons. But that’s only a mere 10 Saturn Vs.