An asteroid will hit Earth at some point. What can we do about it?

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As of yet, there's no known weapon system capable of shooting down asteroids in the minutes or hours before impact, because of their sheer velocity.

And exploding a large one too near - where most of the material still hits but as smaller objects - can be as bad or worse than a single impact. Not so big local and tsunami effects but potentially multiple localities and potentially major atmospheric heating. The Chicxulub impact is thought to have sent so much hot ejecta material around the world that forest fires on the other side of the world were started by the downwelling heat.

Early detection is crucial, obviously. For objects inside the solar system with Earth crossing orbits - which should be most of them - the potential is for finding them with a lot of time to act. For tracking there is the problem of enough precision - deflecting something that potentially could hit too early or with limited deflection capabilities risks sending something that would not have hit into a worse trajectory.

NASA thinks they have identified all the objects of planet killer size within the solar system, with none presenting danger. Tracking ever decreasing sized ones, big enough to be major disasters is a significant, long running undertaking - but it is the most public supported space agency goal. Way ahead of colonization or even crewed missions. I am sure other nations can and will contribute if their observatoreis already don't. A significant impact any time soon would be a powerful motivator - not that we should need to suffer a major disaster to know prevention will be worthwhile; foresight should be enough. A long way between tracking and having the ability to act of course.

Those with known orbits offer opportunity to match course, possibly on their passage around the sun, possibly using solar electric propulsion whilst going the same direction, to have time to dig bombs in deep for explosive dismantling or to change it's direction, or set up thrusters or try Gravity Tractors (keeping a spacecraft within it's gravity well, boosting at precisely the amount to stay at a fixed distance).

But there are the ones coming from further out, that aren't in known orbits, that won't give long warning. They will also offer less opportunity to make use of any solar propulsion or solar energy in the inner solar system and the delta-v for matching with it far enough out (rather than hitting it, shooting it ) can be very large.

Different types of objects and different orbits, different approaches. Different for something that crosses on the inward part of their orbit and one that would cross after passage around the sun on the outbound trajectory. Some, especially comet types, might be deflected simply by spraying black over them to promote outgassing - or white to reduce outgassing.

Or send industrial versions of those auto ball throwers and robots to load them - to toss material out to space.

But I think nothing will deliver more energy with less payload than nuclear weapons; having them used for good to prevent destruction would be different.
 
Ken, for the case of a comet or some other extra solar object coming at Earth from way beyond Jupiter with little warning time, my suggestion would be a very powerful laser aimed at it to slow it down a bit by making it sublime off some of its ices in the direction of Earth. If we had the laser ready to go, it would be fast to use. There are some incredibly powerful lasers being developed already, some for fusion research and some probably for weapons use.
 
a very powerful laser aimed at it to slow it down a bit by making it sublime off some of its ices in the direction of Earth

Until there is a known, imminent threat getting international agreement to build such weapons of that power and have them sitting waiting in space ready could be problematic. China and US that might be capable of it would be suspicious of the other's motivations - and they would probably both be right to be until relations are on a steadier footing. Not that sending nuclear or other weapons into space won't involve getting international consents. On the other hand meteorite defense is likely to be the sort of program that will need to outlive near term geopolitics and might be seen as a legacy, to exist in perpetuity and I think should be international.
 
Both China and the UK have some serious lasers already. See https://en.wikipedia.org/wiki/DragonFire_(weapon) and https://www.livescience.com/61562-laser-china-rip-vacuum-antimatter.html . The U.S. is also working on them.

One thing about a laser weapon in orbit is that it is a sitting duck of a target for another laser weapon on the ground, which would probably have better shielding. So, I doubt that an international group setting up a one laser defense system to use against comets would be a problem getting acceptance. There will probably be plenty of similar weapons on the ground by the time we can get one into orbit. For one thing, they require a seriously large power source.
 
Can we assume an incoming rock will be on an arc trajectory?

Depending on the orientation, if we introduced a spin, would that change it's arc? Or if we change the rate of an existing spin, would that change it's course? Could we pin one with angled jet packs? And light them up?

A clean flower solution.

I still want to see a nuc in space. Think any would notice? What if it exposes something that we don't detect? Haven't even thought of. Come on.....where's your startrek? Think of what might be possible. What happens when you see matter moving faster than you thought it could?

You might be researching inertial dampeners.
 
Can we assume an incoming rock will be on an arc trajectory?

Depending on the orientation, if we introduced a spin, would that change it's arc? Or if we change the rate of an existing spin, would that change it's course? Could we pin one with angled jet packs? And light them up?

A clean flower solution.

I still want to see a nuc in space. Think any would notice? What if it exposes something that we don't detect? Haven't even thought of. Come on.....where's your startrek? Think of what might be possible. What happens when you see matter moving faster than you thought it could?

You might be researching inertial dampeners.
Regarding trajectories, anything not aimed at the Sun dead-center will be some sort of "arc". For things coming in from outside our solar system, they will be hyperbolic arcs, which just bend to some degree as they go around the Sun and then go back out into space, never to return. For things that are part of our solar system, the "arcs" will be closed elliptical orbits (although some of them could be so elongated that they almost look like open parabolas if they come from far enough out). Whatever the nature of the "arc" trajectories, if we have not seen the object before, it will take some observation time to figure out what its trajectory is. And, if it is an icy body, like a comet, then its orbit will be changed by the Sun heating it and some of the ice turning to gas that works something like rocket exhaust from a retro rocket, slowing the comet down compared to just arcing toward the SUN purely under gravitational attraction. So, stuff that comes at us from the remote parts of the solar system or from outside it will be a surprise, and will be hard to predict until we have watched it for a while.

But, "near-Earth asteroids" are on fairy wide elliptical orbits, which may cross Earth's orbit in 2 places. We can study those for long periods and get pretty good at knowing exactly where their orbits will take them. These are the ones that we can plan for with long lead times.

Regarding "spin" on asteroids and comets, both usually have some rotation. Because there is no air to interact with, that doesn't normally change their trajectories in the way that a baseball can be made to curve by putting spin on it. However, it can make it hard to do anything like put a solar sail or rocket engine on it to change its orbit.
 
10-4. The planets have various inclinations and spins. Orientations relative to their orbital path. But the ones we see are set. With no apparent order. However we've never seen a relative quick shift or rate change, and I wonder what affect this might have. Maybe if we found a slow spinner in the belt, we might play with that spin and see what happens. There is so much about the source and interaction of gravity that we don't recognize, let alone understand. Or have explored. I don't think space can be bent. Nothing there to bend.

Why not actually play with it. We can do this now, let's experiment with it. Let's see if there is a relation between the spin of the object and the orbit of the natural object.

UN-related independent motion? Independent momentum? Cancelled momentum? Or balanced momentum?

It's time to play with it. Maybe we can steer something with it. Something new. And useful.

A series of timed taps might alter the CG and throw it off course. Give it a wobble. Wobble deflection and perhaps wobble steering.