Physics is not my forte so I’m going to ask a couple of questions in hopes that someone can answer my questions.
My starting premise is that there are four axis that need to be equal in order for two objects to impact (X, Y, Z, and time).
So to move an object out of this future intersection, all that is required is to alter the travel of the object. A number of things have been proposed that would alter the objects trajectory, but most require s substantial amount of energy. Perhaps there is an easier way.
What if the project landed a series of small mass engines (say ion drives) around the asteroid and then engaged to fire such that a vector created a small push to accomplish two things. First apply some force towards the center of the object to hold the engine in place. Secondly, angle the thrust on all the engines to create a rotational acceleration on the object. If the object can be rotated, and that rotation increased, then the object will create a pull in that direction. That is if I remember my HS bicycle demonstration correctly. Yes the force will be small but applied over time this should move the object. If the trajectory was set up correctly, it could change the angle of the orbit and eventually either fly into the gravity well even faster.
Am I wrong in my thought process?
One of the ideas for moving the asteroids is to put a low-thrust (but high specific impulse) engine on a vehicle that first swings into proximity with the asteroid to be nudged. The gravity of the asteroid would give the craft a come-hither, and the engine would push against this, thus towing the asteroid in the desired direction.
It’s an interesting idea, but I prefer crash-bang solutions, such as redirecting small debris (a few, to ten meters) using a similar engine, preferably already moving retrograde, and crashing it directly into the target asteroid. The energy delivery would be enormous.