Constant thrusting force vs explosions for re-directing a giant asteroid's course

Question

Background:

SPOILERS

In episode 11 of the Inuyashiki anime, Mr. Inuyashiki, a super-powerful 'robot' made from the technology of an advanced alien race, flies to space in order to stop a "giant" (no exact specification on it's size) asteroid from hitting the Earth. However, his chosen method is shooting missiles at it which, given the size of the asteroid, did not prove very effective. Hiro- another 'robot' that is the same as Mr. Inuyashiki- then joins him and self-destructs in an attempt to redirect the path of the asteroid. From the beggining of the anime we know that the technology they posses in their 'bodies' is enough to "destroy the Earth" as the aliens said. Yet it took both Hiro and Mr. Inuyashiki to self destruct in order to redirect the asteroid enough.

In previous episodes these characters exhibited enough thrusting force (from the thrusters in their back) to safely land a large travelling plane filled with people that was plummeting down without control, but it is not mentioned if that is the full extent of their strength. These characters are completely humanoid in appearance but with a completely mechanized interior.

Question:

Under the assumption that we have thrusters that are as strong in thrust as physically and scientifically possible, created with hypothetical alien technology, but with the limitation of fitting on an average person's back would it be possible for two of such individuals to alter the course significantly enough for the asteroid to not hit Earth? Or would it be more feasible to accomplish the same mission with strong enough explosions?

For simplicity's sake assume that the asteroid is heading straight to the center of our planet and it's size and mass is just enough to theoretically destroy all life on earth and the time that the characters have at their hands is 48 hours. Speed of the asteroid is unknown.

If impossible for the scenario in question, how much thrusting force (and/or over which period of time) would we have to apply to re-direct an asteroid that's large enough to destroy humanity? Would it make more sense to use explosions even though the force from an explosion would be spread in all directions? Or would an entirely different maneuver be more plausible?

Answer 1

To deflect an asteroid, you need thrust. In general, this means you should use thrusters, because thrusters are good at creating thrust.

There are two issues with using explosions to deflect an asteroid. The first is that explosions generally do not do a good job of imparting momentum to an object. They often send particles flying in all directions, rather than just the direction you actually want them to go. They also do not couple well with the asteroid. Thrusters are typically designed to get as much momentum per unit energy as they can. They're good at it.

The second issue is that your materials choices for explosions are limited. Generally speaking, explosives have a very low specific energy (energy stored per unit mass). C4 is good for about 6.7 MJ/kg. Contrast that with gasoline at 46.4MJ/kg, or even body fat at 37MJ/kg. Explosives tend to have lower specific energies because they trade away some of that maximum energy density for the rate at which explosives release that energy on the order of milliseconds.

Between these effects, what you see is that explosives have a low Specific Impulse (Isp), which is a measure of how much thrust can be created per unit mass. Isp is the real variable you should care about. Thrusters tend to have a much higher Isp.

The one exception is when dealing with energy that is hard to unleash slowly. Nuclear energy is a great example. Generally speaking, its hard to make a nuclear thruster. The physics of doing so is simply difficult. This means that it's hard to get access to your nuclear energy slowly. In such a case, it may be better to rely on rapid emission of energy (i.e. nuclear explosions) with all the disadvantages associated with explosions than to simply not have access to that energy at all. I'd definitely want to exhaust all of my thruster fuel first.

There is a theoretical craft known as a Nuclear Pulse Rocket...

Answer 2

I am not an expert on asteroids, but I know that a lot of them are not solid objects. They are more conglomerates of smaller objects rather loosely held. An explosion may just fragment the asteroid into a lot of these pieces. That could amount to turning a problem of one asteroid as a bullet into a shot gun bird shot problem.

Thrust or force is more advised. If you have enough time you do not really need to strap on a rocket. There is about $W~=~1250w/m^2$ of solar radiation and UV accounts for about $250w/m^2$ of that. If you then have an asteroid of radius $R$ here is cross section of $2\pi R^2$. We might then think of putting reflecting foil on the asteroid. The photon pressure from reflecting photons off is $P~=~2W/c$ and with the cosine effect we integrate over the area to get the force or thrust $$ F~=~2\sqrt{2}\pi WR^2/c. $$ For a $100m$ radius asteroid the force is then $.37N$. A possible mass for such an asteroid is then about $2\times 10^{10}kg$. This means the acceleration will be a very small $a~\simeq~2\times 10^{-8}m/s^2$. Now using the elementary $d~=~\frac{1}{2}at^2$ and assuming solar radiation gently pushes this mass for a year this asteroid can be displaced $d~=~9\times 10^6m$ or nearly $10,000$ kilometers. This would be enough to avoid a collision with the Earth.

I mentioned ultraviolet because one could concentrate UV onto an asteroid so as to charge the dust on its surface. This would then by electrostatic repulsion be directed away. Newton's third law could then be used to move this body.

Another approach would be to pull a mass with an ion drive near the asteroid that would then thrust away at a very small velocity. The mass of this $100m$ asteroid is about $2\times 10^{10}kg$. Now consider this ion drive tethered to a mass $m$. The gravitational attraction between this mass hovering near the surface of the asteroid and the asteroid would then be an acceleration $$ a_g~=~\frac{GM}{r^2}~=~1.3\times 10^{-4}m/s^2, $$ This means the ion propulsion system would need to provide $F~=~ma_g$ force to then gravitationally pull the asteroid away. This would require more sophisticated technology than wrapping an asteroid with foil, but this would clearly be effective.