But it would make a cool joint project for NASA and the NSF to fund. Capture a comet big enough that you could mine enough water to make a cubic kilometer sized detector in Earth orbit.

That could probably also wipe out half a continent if you mis-aim it...

Then again, it would look spectacular in the sky!

There are other types of neutrino detectors. Not that it really makes the problem any easier to solve, but this isn't the only way.

That's what I was thinking. They have sent neutrinos from one lab to another with a man-made source and a detector smaller than 1km^3. The idea is to put a strong source in orbit and aim it at an orbiting detector. Over time this configuration would be used to scan the entire planet. Still a huge challenge.

That's essentially the main idea most people come to. Using a source so you can concentrate on specific ones and not get distracted by solar, cosmic, or terrestrial neutrinos. Or you could just use terrestrial ones. But still, that detector is the hardest part to figure out.

Exactly

You might be able to tow it in from elsewhere using a light sail, however. Beyond our current technology, but might be doable by 2100, or sooner with a fortuitous comet trajectory.

And once it is in orbit, how do you propose stationkeeping against exospheric drag? Preferably a solution that will remain reliable for 10^n (n>>3) years.

A cubic kilometer of ice is 9.167e11 kg.

Also, just keep the orbit above 800km, and the light sail will still be able to counteract its own drag.

If the orbit gets too low, turn the ice into rocket fuel and use it to refuel ships boosting into higher orbits.

I'm pretty sure that a cubic kilometer of ice in orbit would have more value in other purposes than as a neutrino detector!

Sure, but as long as it's up there, might as well use it in every way possible.