Slow Retargeting of Near Earth Asteroids
Note: The following needs a lot of rework. "retargeting" in orbital space requires plane or radius changes, and plane changes require delta V applied at the plane crossing, not throughout the whole orbit. Both limit when delta V can be applied effectively.
Simply missing the Earth requires a radial distance that is a small multiple of the earth radius; timed right, the gravitational interaction with the Earth could scatter the trajectory of the impactor so that it hits the Moon a few solar orbits (and Jupiter gravitation field interactions later, exploiting "chaotic" amplification of initial conditions for an impact on the far side of the Moon. Assuming the impactor is coming in from the outer solar system, with a perhelion near Earth orbit, it will be "catching up with" the Earth and the Moon; if we hope to scatter most lunar ejecta away from the Earth, the Moon must be in the "trailing" portion of its orbit so the far side faces the direction of the incoming impactor.
Overall, the conclusion is that the largest impulse is required to make the impactor miss the earth, and finesse and precise orbit measurement and prediction is required to exploit "chaotic" behavior to steer the impactor towards it's final destination. The practicality may depend more on specific circumstances for many real bodies than some generalized "delta V" as I attempted to estimate below.
Science fiction describes a quick spread into the solar system; a century or two. But the solar system has been around 4.6 billion years, and the Earth can survive 0.1 to 0.5 billion years longer without our typical negative intervention. With positive interventions, life and intelligence can fill the solar system for billions of years, and spread throughout the galaxy in that time. Think long term; we are only in a race against our own profligate ways, and accelerated profligacy won't improve our chances.
A less urgent threat is an asteroidal impact. Smaller impacts are regional threats; on millenium time scales, they may kill thousands to millions of people, but not nearly as many as typical usage of the nuclear weapon systems we might briefly repurpose to defledct the impactors. It's better to not have those "tools" and take our chances with peace, then to have them for the remote chance that they could protect us from impacts. It's a balancing of risks, and war is the vastly bigger risk.
Risk is better mitigated (and ultimately eliminated) though a slow but continuous development of sustainable space capability, an emphasis on doing the most with the least. Job one is increasing situational awareness - more data improves our chances better than more megatons. Hyperaccurate data - for example, laser ranging to retroreflectors on every heavy object in the inner solar system, centuries of data to micrometer accuracy - is essential to optimizing our long term survival. "Deflecting" near earth asteroids merely postpones disaster, perhaps to an era when we have temporarily lost the capability to deflect them again.
Fortunately, the Earth is equipped with two superb shields; our Moon, and Mars. With century-scale planning, we can deflect objects aimed at the Earth into the Moon instead. A maximum of 400,000 kilometers deflection, typically less. A century is 3 billion seconds, so a velocity impulse of 13 centimeters per second a century before impact could deflect an asteroid over that distance. With a hundred centuries of preparation, 1.3 millimeters per second, literally a snail's pace.
But "impulse" is disguised bomb thinking. Imagine instead a "small" 100 meter per second solar-powered launch loop, throwing small rocks (most of which become meteorites someday). Assume 10% energy duty cycle; either the solar cells or the launcher will be pointed the wrong way, most of the time (though the loop can store solar energy when available and launch in the dark). How much power would we need to deflect the asteroid hyper-accurately towards a specific, prepared impact site on the Moon?
Assume a 1 billion tonne asteroid, and a 50 year thrust period, of which 5 years (160 million seconds) are thrust, an average of 60 years before scheduled impact. We need 20 cm/s of deflection velocity, an impulse of 2e11 kg-m/s, an average thrust of 1250 newtons over those 5 active years. If we launch globs of mass at 100 m/s, we are launching 12.5 kg/s, about 6 megawatts of intermittent power. At an average distance of 1.5 AU from the Sun, and a PV efficiency of 10%, that is a 10 hectare PV array and 2 million tonnes of ejection mass (centimeter pellets or smaller).
By solar system or biological evolution timescales, a century is an eyeblink. An enduring space-faring civilization will have lifetimes of billions of years, not centuries; threats will be dealt with over vastly longer timescales. The asteroid belt and Oort cloud will be tamed and managed for long term delivery of useful materials to the Moon and Mars. Most asteroidal material is rocky, not much different from the lunar and martian targets. Still, molten glass can be a good construction material, and we will probably "blow giant bubbles" with it, away from the impact zones. The rarer (and far more valuable) iron asteroids will be processed into machinery - quintillions of small mechanisms and magnets.
In a few hundred million years, we run out of asteroids. We've slowly processed the stony material into glass, silicon, aluminum. We have learned to make complex atomic structures that mimic some of the useful behaviors of the less common elements. But entropy and decay will always win; at some point, even if we are vastly more prudent than the "rape the solar system" exponential expansion fantasies of the "century to the stars" crowd, essential rare atoms (niobium, helium, ???) will be evaporated into a solar system too hot to ever collect them into exploitable small bodies again.
From the vantage point of 2017, I cannot envision a solution for a billion years from now. Fortunately, a billion years of a quadrillion mature minds will have plenty of time to fine excellent solutions. It is my job in 2017 to improve the odds that we will mature into those long-duration minds. Near-immortality won't be easy, but that is what accumulated wisdom is for.
Project Pan-STARRS and the Outer Solar System - https://link.springer.com/article/10.1023/B:MOON.0000031961.88202.60