Earth-killer challenge

Question

Related to this question. A lot of the discussion there got sidetracked from the question of orbital physics, into questions about alien motives and what the humans would do, so I want to start a new question with more clear physical parameters and a more well-defined objective.

You have a motor that can exert 100N of force over a very long period of time (at least a thousand years). It may be an ion drive, powered by a large solar panel array, and capable of refining extra propellant from comets and asteroids. It's 1AD, you begin in Earth's orbit, and you want to do as much damage to humanity as you can, by smashing asteroids or comets into Earth with as much kinetic energy as possible. If you can actually kill humanity, that is your ideal outcome. Your spaceship weighs 10000 kg. You can easily compute trajectories to the desired precision. What methods do you use?

Some possible strategies:

• "The drop": take a very massive asteroid or an Oort cloud object and slow it down until it drops out of orbit. Just let it fall to Earth while you move on to the next asteroid.
• "The windup": take a less massive Oort cloud object and ferry it even further out of the solar system, then slow it to a stop when at a sufficient distance. Then accelerate it straight at Earth.
• Suicide run: like "the windup," but without an asteroid. Just get very far from the solar system, then come to a stop, turn around and accelerate straight at Earth. For this purpose we may say the spaceship weighs 10000kg. If the approach phase of the suicide run takes 1000 years, the impact energy will be around 10^21 J, without taking into account relativity. (Chicxulub = 10^25 J). Can be done only once.
• Gravity assist: drive your object past Jupiter so that it slingshots around it, gaining speed.
• Multiple gravity assist: repeat the gravity assist several times on one object.
• NEO wrangling: take an existing large comet or asteroid on a highly eccentric orbit that will pass near Earth, such as Halley's comet or 99942 Apophis. Catch it far from Earth, then adjust its orbit slightly so it hits Earth. This sounds like a good plan to me, although it is limited by the number of such NEOs.
• Simultaneous targeted attack: set up dozens of objects precisely targeting cities, timed to strike in rapid succession and wipe out all the major cities on Earth.
• Moon tugboat: take a small moon and drive it towards Earth. (sounds not feasible)

Targeting strategies:

• One big hit causing an extinction event. Chicxulub-scale energy (10^25 J) would definitely do it, if you can get there.
• Multiple Tambora-sized hits (10^20 J) to affect the climate globally. One would need a lot of these in rapid succession to cool the planet enough to cause extinctions.
• Many smaller nuke-sized hits to wipe out cities (such as 10^15 J).

If you're still around past AD 2000, we can assume humans will be causing problems for you, unless you've already done substantial damage or are already moving too fast to be stopped. AD 2500 without doing damage = Mars is colonized, game over.

Please no answers without a back-of-the-envelope calculation of feasibility, the impact energy, and time required. See TNT equivalent for some examples of different energetic events for comparison. Also wolfram alpha is great for unit conversions.

Answer 1

Forget the rock, just ram the ship

As others have pointed out, because you have a constant force of acceleration if the smaller the load being accelerated, the higher the kinetic energy of impact.

For maximum impact, accelerate straight outward, and do a 180 at the halfway point. Since the inbound trip does not have a turnover, the average velocity will be higher inbound, so you actually want to spend about 1171.5 years outbound and 828.5 years inbound.

On earth impact, your impact file be about 3.417E20 Joules, which is about 5.7E6 Hiroshima bomb or 1512 Tsar Bombs, but only 0.003 Chicxulub impacts (using a more accurate 1.15E23J figure). Though this will be a bad day for many, it's not nearly enough to wipe the planets clean of humans.

Ignoring special relativity, I computed that the impact velocity was about 0.087 c - so ignoring relativity is close enough approximation.

10000 Kg sounds like a lot, but Chicxulub mass est. is 3.2E15 kg. But you really don't have the time to push around a big rock. Assuming you could find another Chicxulub, you could not even apply 1 mm/sec of delta V in 2000 years. Not enough to change a suitable near-Earth object.

Answer 2

(...) you want to do as much damage to humanity as you can

You're on the tight path with that device.

by smashing asteroids or comets into Earth with as much kinetic energy as possible.

This is wasteful and inefficient.

If you can actually kill humanity, that is your ideal outcome.

Let me propose that you simply do a lot of nothing for a while. Let humanity do its thing until they start exploring space.

As soon as they start making artificial satellites, make a few round trips to the Moon. Those monkeys are gon'na flip! They will start creating cults about you, which is when the damage begins.

Now let them develop their technology. You can let them approach and study you but don't get captured. The moment you notice they have a great lot of noisy satellites, start smashing them. Orbital roadkill will turn each satellite into shrapnel, which has a domino effect. Bonus if you end up killing some human astronauts.

This is when humans flip again, and this time they understand it's war. They might wish to nuke you in retaliation when they find out you're the culprit for their space losses, so go to Martian or Venusian orbit for a while.

Humans will develop their war technology extremely fast. Forget about mere ICBM's, they will.have interplanetary bombs with enough yield to require you to update your global maps whenever they are used.

Now you can just sit and wait. It's a matter of time until political strife causes them to use these new weapons on each other, eventually wiping themselves out. You can either sit and wait, or give them a nudge by going back to Earth and aggressively lithobreaking onto one of its largest cities.

Answer 3

Attack with only asteroids of extremely low albedo or potent greenhouse gases.

Forget about targeting cities. Forget about tnt equivalent. Forget about using asteroids only as a store of energy to be released in impact. See the asteroids as a store of materials.

I'd suggest a good thing to read up on is how we could teraform mars. In that field, theres some really useful ideas on how we can rapidly heat a planet using cleverly crafted asteroid impacts directed by a low power engine.

Essentially your alien uses asteroid impacts to teraform the earth onto the global warming runaway greenhouse hell were currently trying to avoid.

Select black asteroids, typically high carbon and ultra low albedo, and smash them into the pristine white Artic, Antarctic, and anywhere else on the planet that's nice and high albedo.

By covering or replacing white shiny ice with pitch black soot or something else dull black, sunlight stops being reflected and is absorbed as heat.

Your turning the artic from a shiny mirror into a black road on a hot day. Depending on how black your black is - you could turn each square meter of earth s surface you cover into upto a 1.3kw solar heater. If you can use tiny asteroids that each cover just 10sqkm in dust per hit, that's a peak of 130 megawatts of heat generation from that point onwards, (although ~80 is more reasonable due to low sunlight angle and poles being further from the sun than equator). That's a lot of heat.

(You can also use ammonia or methane, both of which are plentiful, as these will build up the greenhouse effect directly and are substantially more powerful than co2.) But bang for buck on your single engine accelerating I'd suggest put all your energy in painting the planet black and making it suck up as much sunlight as possible.

Excess heat at the poles causes tundra melt; releasing methane, a greenhouse gas significantly stronger than co2. This forms positive feedback (releasing more methane faster) amplifying the greenhouse effect. There are lots of other positive feedback processes going on as well, dozens at least - another is more heat causes more bushfires and blackened forests absorb more sunlight than green ones did, raising the temperature more causing more burning, and more burning releases more co2 raising the temperature even more.

We dont know how bad all these runaway processes can get; possibly to venus levels. But even if it doesnt get that bad, you'll wipe humanity out with floods (900m sea level rise), firestorms, hurricanes (every degree in warming makes hurricanes more likely and stronger), kill off all our crops, or just directly wipe us out with heatstroke.

Answer 4

Here is one option: near Oort-cloud line drives.

The plan:

1. In the near Oort cloud at 2000 au from Earth, pick an object of mass 5000 kg.
2. Objects in the Oort cloud are moving at a few km/s. Bring the object to a stop.
3. Accelerate the object straight at Earth, separating from the object as late as possible to drop it on a city.
4. Pass close by earth (at very high speed). Take photos of Earth's surface to determine the next target.
5. Decelerate until you are again stationary in the Oort cloud at 2000 au, on the opposite side of the solar system.
6. goto step 1

Analysis:

1. Total K.E. of spaceship + object just before release is Force * Distance = 100 N * 2000 au. Mass of spaceship + object = 15000 kg. The spaceship's mass accounts for 2/3 of the kinetic energy, so we divide kinetic energy by 3 to get the object's impact energy of 100 N * 2000 au / 3 = 10^16 J, enough to kill a city.
2. K.E. = 1/2 m v^2 , therefore v = sqrt(2 * 100 N * 2000 au / 15000 kg) = 1997 km/s. Since this is much faster than the orbital speed of Oort cloud objects, the time it takes to stop the object in its orbit can be neglected.
3. distance = 1/2 a t^2, so time of approach = sqrt(2 * 2000 au / (100 N / 15000 kg) ) = 9.5 years
4. The return trip to the Oort cloud can be a little faster than the approach to Earth because we weigh 10,000 kg instead of 15,000 kg. That means we can keep on accelerating for a little while as we pass Earth before we turn around and start decelerating. A lower bound on the return time would be sqrt(2 * 2000 au / (100 N / 10000 kg) ) = 7.75 years. Maybe it's really 8 or 8.5 years - no need to be too precise.
5. So, we destroy a city roughly every 18 years, plus whatever small time it took to find a suitable object and stop it.

Regarding the mass of the object: if it were lighter than 5000 kg, the time needed could be reduced by up to a year, but the impact energy goes down rapidly because more of the kinetic energy is going into the spaceship and not into the object. If it were much heavier than 5000 kg, the impact energy could go up by nearly a factor of 3, but it's already 10^16 J which should be enough. More significantly, heavier objects increase travel times by a lot. If the object weighed 100000 kg the approach trip would take 25 years, for a total trip time of 33 years.

Although... perhaps this would be worth it, if the big object could actually be a cluster of 10 objects that we separate before impact to hit 10 cities at once. Keeping the cluster together as we accelerate it, and separating it once we're done, might be a problem if the spaceship lacks tools or an EVA robot.

But perhaps the spaceship could just stack the objects in a long line in front of it, like scoops on an ice cream cone, so they are held together by the pressure of acceleration and easily separated when it's time. Wouldn't be easy, but if it has the dexterity to do that, I think humanity is toast. So maybe it would be necessary to reduce the drive to 10N instead of 100N, or just to say that the scout's computer is programmed for orbital dynamics and not for that kind of stacking.

Answer 5

De-orbit the moon using leverage.

There it is, hanging over us. If the moon came down that would be it for life on earth.

I propose your alien could produce a series of impacts, finally impacting the moon adequately to slow it down and so bring its orbit into its Roche limit. It would be torn apart from gravitational forces and rain down on the world, Seveneves style. The consequent superheating of the atmosphere would shed it into space.

The plan is taken from my answer to this idea. How might people try to stop the world becoming a rogue planet?

an AI ... that knows the site, mass and velocity of all objects bigger than 10 kg in its immediate vicinity. There is a mass of comparable size which could be made to intercept and gravitationally deflect the incoming mass. But the interceptor mass is itself very large. To move it will require a different mass of comparable size. A smaller such mass is available and correctly positioned. Although smaller, this mass is also not easy to move. A mass smaller yet is also in the correct position...

Your AI presents a series of 12 successively larger gravitational interactions of which the smallest and first is within the ability of humans to achieve with rockets. In a planetary billiards chain reaction, an array of progressively larger objects will change course, with the end result the gravitational deflection of the incoming impactor.

Your alien sends an asteroid into another larger one, with the goal of changing the course of progressively larger objects. The final one hits the moon and slows it down in its orbit, ultimately causing it to come down.

Answer 6

If you have a limited energy budget and can use any mass as reactive propulsion and use it to change trajectories, combining your comments and my suggestion in comment section

Then to amplify the energy you have, a potential strategy could be as follows:

Search for a proper object in the vicinity of 0 to 11 km/s delta-v, use most of it as reactive mass with lowest possible Isp (thus most or your energy goes into the future impactor).

Then you can amplify your energy by $({\frac{\Delta v(\mathrm{earth escape velocity})}{\Delta v(\mathrm{source, Hohmann first transfer maneuver})}})^{2}$.

Sorry for the lack of concrete numbers and a suitable asteroid, but a reasonable expectation would be 10-20 times the impact energy.

A gravity assist maneuver to Jupiter starts with $\Delta v$ 9.36km/s if from Earth, but it is reasonable to expect the ability to change rotation(orbital direction) of a projectile and then instead of earth escape velocity we may have earth orbital speed multiplied by 2, or something like that, in the formula. Which could definitely be an improvement in terms of amplification if a suitable object were found closer to Jupiter (or another gas giant).

There are some theoretical limits to gravity assists, it is not possible to bounce back and forth indefinitely, increasing the energy each time.

All that takes a few decades at most, so you may already see a distinct difference between defining things by force or limited energy.

Superiority of AI (aliens)

Can there be some showoff case of superior being that blows the mind, like creating some cascade effect on given energy budget which results in a given timefame is many many orders of magnitude amplifies the energy they had initially?

Like making subtle changes to many objects in asteroid belt, so they start to influence each other and interacting with changes of gravity field of solar system and then at day D start spewing asteroid after asteroid on collision course with earth?

Good question! IDK.

In such extravagant form the answer is no. But in therms of amplification of initial energy it hard to tell. Lagrange points can be of interest - what if the whole belt would be collected at L3 L4 (just a litte push and pull to 2 halfes of each asteroid) - one invests energy in such change but it is not lost but collected in these points and can be extracted back, so one big change for free. Can it be helpfull, idk, needs more brain power. But gravitional binding energy of whole belt (4% of moon mass) can be around 1e26J, with a potencial of that energy be concentraed in some small chunk of the asteroid belt to continue its destruction jorney. Definetly there is some potencial, but timeframe and all that is hard to tell.

Frame challenge

Not exactly a frame challenge, and more like opinion, comment to that alien thing.

I would say that any tech savy human, with a proper university education or diy guy, or one which focus on computer and technology - having a space ship with 1000km/s delta v, having time 2000 years - can not only destroy humanity in give time rame, not only incenerate surface of the planet, but as bonus make bunch of glass beads out of the whole planet.

What he needs is his basic tech understanding/science, freedom to act in space and copy of WB questions and answers. Copy of wiki also can be helpfull, but not like a copy of WB.

So even if alien chose 3th option, that belt thing, I won't be impressed by them, I basically won't be satisfied by any outcome except steamrolling the whole solar system.

Answer 7

Plan 9

I was hoping someone else would come up with this idea, because I don't know enough to flesh out the details.

The idea is let the gravity of the Sun and the Earth do most of the acceleration of the rocks. Fly out to the asteroid belt (or possibly Kuiper or Oort regions). Pick a suitable rock. Deorbit it from the Sun such that it collides with the Earth. The combined fall towards the Sun/Earth will give rocks plenty of speed (slowest for asteroid belt, highest for Oort cloud) to leave their mark on the Earth. Time to impact is at most 100-150 years assuming you are not deep in the Oort cloud.

Since all you are doing is deorbiting the rock, you spend as little as time as possible maneuvering each rock. Since Oort objects have smaller orbital speed than asteroid belt objects, they are quicker to de-orbit as well as falling from a greater height. Given the reduced deorbit time and increased impact velocity, I suspect Oort objects are your best source.

For bonus points, instead of deorbiting them, you just the put the rocks into highly elliptical orbits that all happen to intersect Earth's orbit on Jan 1, 2001 0:00 UTC distributed all over the planet - You need to be very good at orbital calculations - in reality the chaos of the problem makes this impossible unless you have God-like knowledge of everything moving anywhere near our home star.

You want to accelerate small rocks because your thrust is so low large rocks can't be moved quickly enough. If your rocks are too small, they will burn up or slow down or simply be too small to do lots of damage - I did not attempt to figure the ideal size.

So, my major unknowns are 1) Best object source - though I suspect it is the Oort cloud), Best object size, and how long it will take to deorbit each object on the average (avg. distance between the desired impactors is unknown)

I could easily envision that you could deorbit many hundreds, or perhaps thousands of objects that could level a city, but I don't have the info to back it up.