Your toenail is affecting the asteroid's trajectory, by laws of physics. That adds nothing to this conversation.
There! That's what I was looking for. So they were expecting a miniscule change, and instead they were pleasantly surprised by the evidence and are now expecting a very tiny change?
They are hoping to see a change in its velocity of a fraction of a mm/s.
https://youtu.be/U0nZvOm3bNs?t=415
It is a small value, but its a measurable fraction of the the velocity of its orbit around the primary (about 12h).
They know the momentum that the impacter had. They had an estimate of the mass of Didymoon and its velocity. They are interested in how much of that momentum was transfered to Didymoon and how much was carried away from ejecta.
I think the real takeaway here is just that something unexpected happen. They're monitoring as they would have regardless, and results will come in time. Expecting results and/or a conclusion this early is, well, jumping the gun.
You know, I have my doubts about the practical benefits of this whole operation given that there aren't any planet killers lurking in the asteroid belt for at least a century, and so I suspect this was sold with a planetary defense angle because a bit of a scare is a good way to loosen the pocket book. That said, maybe we could justify rebuilding Arecibo along similar lines. I believe they were in fact using it as a near Earth radar gun and it was even initially constructed as a defense project.
The mission as approved 3 years before Arecibo collapsed and final assembly of the spacecraft was done half a year before. https://cosmosmagazine.com/space/dart-timeline-from-build-to...
The loss of Arecibo was a loss to the mission as the pictures that you most often see of Didymos were from Arecibo.
The mission itself was also a technology demonstration of a camera, autonomous navigation using that camera, solar arrays, new antenna, and ion thruster design. https://en.wikipedia.org/wiki/Double_Asteroid_Redirection_Te...
2. China has an Arecibo-class device. Actually bigger than Arecibo. Do we need two? Considering that the whole Free World could not scratch together enough money just to maintain Arecibo, building it again seems beyond possibility.
I'm not all that familiar with any of the big radio telescopes, but I thought that China's didn't have the active radar capabilities that Arecibo did. That said, I find it sad that something like Arecibo was possible to build and maintain in the 60's but not now. I suppose that has to do with the perception of it moving from defense project to science project.
That said, I would think runaway climate change or nuclear war are much greater threats to civilization (though humanity would probably survive in some form), so those are probably where the effort should go if survival of human civilization is your thing.
One struck the ice sheet in Canada only 12,800 years ago that wiped out 30+ genera in North America including camels, horses, cheetahs, mammoths, mastodons, giant ground sloths, dire wolves, sabertooth cats, a giant beaver, and a giant bear. Their bones, and Clovis spear points, appear only below a thin stratum with massively elevated platinum concentration.
Radar is just a matter of putting the right antenna horn on the focal carriage, wired to appropriate gadgetry.