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That can be pretty easily determined. And the earlier the effort is undertaken, the less the effort required to deflected it enough to miss. (sort of like global warming)
Pushing the whole thing is a plausible approach, hopefully it's a not pushed into another impact trajectory.
The objects are often in pieces already which are only loosely bound by gravitational attraction into a "Rubble Pile". You can see pieces already there in this image of asteroid Itokawa:
originally posted by: Ophiuchus 13
Space drone group or crafts approaches potential impact object surrounds or attaches to potential impact object P.I.O
Water-jets cut at engineered cut points to separate P.I.O into pieces.
The moniker rubble pile is typically applied to all solar system bodies with Diameter between 200m and 10km - where in this size range there is an abundance of evidence that nearly every object is bound primarily by self-gravity with significant void space or bulk porosity between irregularly shaped constituent particles. The understanding of this population is derived from wide-ranging population studies of derived shape and spin, decades of observational studies in numerous wavelengths, evidence left behind from impacts on planets and moons and the in situ study of a few objects via spacecraft flyby or rendezvous. The internal structure, however, which is responsible for the name rubble pile, is never directly observed, but belies a violent history. Many or most of the asteroids on near-Earth orbits, and the ones most accessible for rendezvous and in situ study, are likely byproducts of the continued collisional evolution of the Main Asteroid Belt.
In the past decade, scientists have confirmed that many asteroids are not solid rocks, but are instead cosmic rubble piles made up of jumbles of rocks. Researchers typically suggest that these asteroids stay together due to gravity pulling them into clusters and friction locking them in place.
Asteroid 1950 DA is covered with sandy particles known as regolith
If an approaching asteroid were detected early enough, it could be possible to divert its path using the gravity of a spacecraft. Instead of sending an impactor to ram into an approaching object, a gravity tractor device would fly alongside the asteroid for a long period of time (years to decades) and slowly pull it out of Earth’s path. Gravity tractors would be most likely to work on any shape or composition of approaching asteroid, even if it were just a pile of rubble.
If it's a rubble pile as many are, pushing on it could be a bad idea if it could break the object into pieces, because then you have multiple objects to deal with, instead of just one loosely bound rubble pile.
originally posted by: SaturnFX
better to just send a rocket up with a thruster to push it out of the way...assuming you can land on the asteroid...the further out the better as it would require less fuel, but of course, the harder it would be to target it to begin with.