Just for clarification, it sounds like you're asking, in addition to asteroid tracking, about a possible astronomical explanation to Crucifixion Darkness. That would require a collision in transit between the Earth and the Sun that would make a debris cloud large enough for 3 hours of shade.
Such an astronomical event would be very rare because asteroid on asteroid collisions are rare and this one would need to be precisely timed and placed. Ideally you'd want the debris field to be moving in roughly the same direction as the earth relative to the sun, to maximize the shading period of time. Such an event is extremely extremely unlikely but not impossible.
I am interested in learning the locations and velocities of the near
earth asteroids at the time of the crucifixion of Jesus Christ.
The NEO Program has greatly increased the tracking of Near Earth Asteroids. Current estimates put the number of 1-km or greater asteroids at 981 +/- 19. Smaller asteroids, the number grow exponentially. Smaller asteroids are harder to see. According to this, 16,000 have been identified and there are thousands more.
As pointed out in the other answer, Near Earth Asteroids are subject to gravitational perturbations and that makes predicting their location a couple thousand years ago quite difficult, especially if they make more than one close pass to Earth because orbital changes get amplified with each pass, the closer the pass, the greater the amplification of uncertainty. Tracking thousands of asteroids back nearly 2,000 years is an enormous task.
any was between the earth and the sun at the time of Jesus'
crucifixion on Good Friday.
Asteroids are too small to block the sun in any meaningful way. We only study near Earth Asteroids to be prepared for collisions. Other than the occasional collision (and possible space mining), Near earth asteroids are astronomically boring objects that are too small to see. They would have gone mostly unnoticed to anyone before telescopes because they wouldn't have been visible, even in transit.
a clustering of asteroids on Good Friday between the earth and sun. If
so they could be the remnants of a gigantic collision that would have
been capable of making a dust cloud in interplanetary space that could
have produced a shadow on the entire earth which would account for the
observations reported by the gospels and the Chinese astronomers and
St. Dionysius and others.
Asteroids don't "cluster". They're too few and too far apart. A collision of two is possible but rare. A cluster of many, enough to block the sun for 3 hours is impossible.
Asteroid collision and a dust cloud is an interesting proposal. Unlikely but worth exploring.
Here's a question about asteroid collisions with other asteroids in space. While it's believed that they happen, they're rare events.
From the answer:
inter-asteroid / asteroid-comet / inter-comet collisions are extremely
rare. They are in fact so rare, that there is basically no statistics
about it. It is hard or near impossible to put a number of that.
However, there are attempts to predict collisions. Keeping in mind
that orbital parameters of small and distant objects can only be
determined with some uncertainty, the idea is to go through the
database of known objects and predict when a pair of objects comes
into a certain proximity. This gives candidates for collision events.
They are rather interesting for researchers, who are studying the
structure or chemical composition of such objects. Another however,
the amount of collisions actually happening after such a prediction is
still incredibly low.
So, while we know that asteroid on asteroid collisions do happen they are so rare that none has ever been observed. For such an event to block out the sun, you'd need a couple very large asteroids, and the collision would probably need to be quite close to the Earth and in ideal placement between the Earth and the Sun where the debris field moved in relation with the Sun and Earth so as to maintain a shadow.
And the collision would need to be high speed enough to create a large spray of dust, so not a glancing blow, but a full on impact. That's improbabilities on top of improbabilities.
Meteor and comet trails (not to be confused with comet tails) follow an elliptical orbit. Those are easy to trace back to their origin because all the debris is lined up and orderly.
Collisions behave very differently and you'd need a sufficiently large high speed collision to create any kind of large dust cloud to create 3 hours of shade on Earth. Tracking debris from a 2,000 year old collision is very hard without having that debris in hand - then, maybe.
An impact crater is what the footprint of a collision looks like. (Resemblance to the Death Star is purely coincidental)
This is what a larger collision looks like (no longer visible to the eyes but detectable by gravitational and crustal density anomalies.
This is what an even larger impact looks like, where you get enough debris blown off where it forms into a moon.
Explanation (scroll down to giant impact)
It's thought that Binary asteroids sometimes called double asteroids or asteroids with a moon are relatively common, and may be the result of impacts, but there in lies one problem. A 2,000 year old impact might just look like a binary asteroid. It wouldn't be possible to discern the date of the impact just by telescope and orbital tracking, but statistically a 2,000 year old impact would be abnormally young.
Finally, the largest, highest speed collisions, the two objects would just blow their debris apart - and there would basically be nothing to detect 2,000 years later. Debris from a collision would either coalesce back into an asteroid or binary asteroid by gravity or simply drift apart. In either case, evidence of a collision wouldn't be obvious outside of some hands on analysis of glassy compounds formed by impact or other chemical studies, but we'd actually have to get the debris into a lab to study it that closely. By telescope, there would no evidence of such a collision and debris cloud after 2,000 years. Any debris from the cloud would look just like all the other space dust with nothing distinguishable about it at least by telescope.
The other problem with finding a theoretical impact that you're looking for is that you can't limit it to near earth asteroids. Any comet or longer period asteroid that crosses the Earth could have had such an impact and any evidence of that comet being impacted would have left with the comet as it flew past the outer planets long ago, perhaps changing it's trajectory so it's no longer an earth crosser. The number of objects to look for grows enormously when you consider that one of the objects could have come from much further out.
A third problem with your theory is that such an impact, close enough to cause visible shade would very likely shower the Earth with debris and that would have been noted in the history books as well as a meteor shower like none before or since.
A long or medium period comet being struck by an asteroid might be a better explanation as the icy body being impacted would create a dirty gas cloud of some size while reducing debris impact on Earth as much of the ices would melt into gases and disburse under the sun's rays. That would decrease the showered by meteors problem, but make finding the impacted object even harder.
Your space impact idea is a clever attempt to explain crucifixion darkness, but astronomically speaking, hugely improbable. And the answer to your question is that evidence, if such an event did happen, would be very hard to detect, and with current technology, probably impossible. Good question though.
Another way to think about evidence is that, when a collision happens on a planet, the planet's surface is relatively static and the record is preserved. Obviously there's some weathering but information can be deduced by impacts that are hundreds of millions of years old. In space, in the solar system, everything moves. Things fly apart from each other while orbiting the sun. A two thousand year old collision in space, even a large one, might leave no detectable record after 2,000 years, or if one object survived it could be virtually anywhere in the solar-system 2,000 years later.
Hope that helps.