# What would a relativistic kill vehicle hitting the moon look like from earth?

For some reasons aliens wanted to kill off humanity, and therefore they sent a relativistic kill vehicle to Earth, with enough energy to destroy all life on Earth. However they slightly mis-targeted and hit the Moon instead, on the border to the far side, opposite to the sun, impacting vertically. Assuming this happens at half-moon, what would people on Earth observe? Would they survive the event, or would the heat from the Moon kill them anyway?

• Possible duplicate: XKCD What-If? #20. ;) – Frostfyre Jul 19 '16 at 19:24
• Not really, as that one is about hitting earth. To start with, there's no atmosphere on the moon. – celtschk Jul 19 '16 at 19:26
• Same basic principles though. – Frostfyre Jul 19 '16 at 19:57
• I doubt the presence or absence of an atmosphere would make a significant difference at relativistic speeds. It would have been interesting if Randall would have had some example in between $0.01c$ and $0.99c$ -- say, at $0.8c$ or so. – a CVn Jul 19 '16 at 20:19

This probably depends on the type of impactor. For a relativistic kill vehicle, the aliens can either accelerate a small vehicle to a high relativistic speed and slam that into Earth, or accelerate a much larger vehicle to a much lower speed, and slam that into Earth. The effects of either of these vehicles hitting the moon will be very different, since the manner in which they release their energy will be very different.

Small, fast vehicle:

Let's assume, in both cases, that the energy is equal to about 100 times the energy of the Chicxulub impactor, a.k.a the asteroid that killed all of the big dinosaurs.

The energy of the particles thrown out by the impact of our theoretical impactor will increase as the energy of the impactor increases, so a small, fast vehicle will create more of a small, high energy explosion. Let's assume that this energy is then radiated out in a spherical shockwave of radiation. The moon is 384 million meters away, so the sphere has an area of around $10^{18} m^2$.

Our impactor has a total energy of around $10^{24}$ J, so this will be the equivalent of around \$10^6}W of energy striking the atmosphere if it all hits in about a second. That's about a thousand times the energy of the sun, but only for one second. The intense pulse of radiation will likely flash burn the half of the Earth that can see it, probably killing or at least badly burning anyone that's outside if they aren't underwater, though I'm not entirely sure how much energy a human can absorb in a second and live, so that might be wrong.

Of course, the vast majority of the energy has been radiated away from the Earth, and there won't be any aftershocks, so many people on the "night" side of the Earth are likely to survive.

This is also a bit of a simplification, since a relativistic impactor would burrow into the Moon a decent distance and probably dump the majority of its energy into the mantle of the moon, where it would cause less damage to the Earth, so this is something of a worst-case scenario.

Large, slow vehicle:

If the aliens instead took a ball of rock 100 times the size of the Chicxulub impactor and slammed it into the moon at the same speed as that asteroid hit Earth with, the effects would likely be different. Rather than high energy radiation, most of the energy would come in the form of a huge ball of gas and debris expanding away from the impact site. There would be a lot more mass fired out of the moon by this impact, but it would be fired out at a much lower velocity.

Some of the debris would probably hit Earth, which would see something like a global meteor shower with a few bigger impacts here and there. These wouldn't come all at once, but instead rain down over a few days. At worst, the Earth would be peppered with dozens of atomic-bomb sized explosions as large chunks of moon rock rain down into our atmosphere.

Most of the debris, though, would fall back to the surface of the moon, leaving a giant crater with a molten center, or else would fall into orbit around the Earth. The Moon would gain a big glowing spot and the Earth would gain rings, at least for a little while.

In neither case, however, would the Moon be destroyed or even knocked out of its orbit. A 100x Chicxulub impactor, while definitely big enough to absolutely wreck the biosphere, only carries about 0.1% of the orbital kinetic energy of the Moon in its orbit around Earth, and less than 0.001% of its gravitational binding energy.

• Your energy for the fast option is too high--you're assuming a spherical shockwave but half of that is blocked by the moon itself--thus cutting your energy in half. Also, the energy release is going to be mostly below the surface, blocking just about all of it. The Earth will only get hit by the glow from the plasma kicked up by the impact. – Loren Pechtel Jul 19 '16 at 22:32
• @LorenPechtel I wasn't sure how far in it would burrow, or how much of the shockwave would pass through the moon, or exactly what shape the high energy particle plume from a relativistic object punching into the surface of the moon would take (which I assume would probably be velocity dependent?), so I made an "assume the elephant is a point mass with zero friction" type assumption :) – ckersch Jul 20 '16 at 0:12
• It wouldn't take much burrowing to put a lot of moon mass between the energy release and the Earth. Anything liberated more than a few feet down would not shine on Earth unless it happened to hit a peak. – Loren Pechtel Jul 20 '16 at 3:17
• Ten to the how many? See unformatted LaTeX – Mark C Apr 17 at 14:29

with enough energy to destroy all life on Earth

This needs a little calibration, Do they want to cause a mass extinction, or kill most life, or kill all life, even the extremophile bacteria that live in all kinds of weird environments. XKCD What-if #20 provides a handy guide to the kind of speeds and damage involved. Hitting the moon reduces the damage to Earth somewhat, but only somewhat.

If they just wanted to cause a mass extinction, a hit on the moon doesn't do an awful lot to Earth. People who happened to be looking straight at it might well be blinded, and quite a few fragments will hit Earth, which might kill a few thousand to a few million people, depending on where they hit. Civilisation will survive, although it's taken a knock.

If they wanted to kill most life, by melting the crust, things get rather more messy. Quite big chunks of the Moon will hit Earth, and we'd have a mass extinction. Civilisation will largely collapse, and a billion-plus people will die due to the collapse of trade and transport, followed by diseases breaking out, and so on. But humanity probably survives, and if not, some other species would evolve into our niche within a few tens of millions of years.

If they were going for the full-scale planet-smash, Earth as a ball of rock will probably still be there afterwards, but the oceans and a few tens of miles of the crust will have boiled off, and all life is probably gone. Shoot hard enough, and a miss may still do the job.

• They didn't hit the moon deliberately--he's talking about the moon getting in the way and taking the hit meant for the Earth. – Loren Pechtel Jul 19 '16 at 22:29

I'm not certain there is enough hard information to come to a truly solid answer, for example, this 'relativistic kill vehicle', what are the mass and velocity of the object? Does it strike head-on, or at an angle, etc...? As far as the view from Earth, regardless of object parameters, almost half the world won't see it at all, as they are facing the opposite direction, those with a view would likely see a brilliant flash ( think Megatons +), with any other side effects of impact taking between seconds and days to reach Earth. Those side effects are determined by your parameters. -Hope this helps...

Frostfyre, I was thinking of XKCD's relativistic baseball, with the bleachers set [relatively] "safely" down on Earth. It might provide a decent metaphorical starting point (though I suppose that Project Thor might be a more realistic example).

celtschk, it would very much depend upon the size and mass of the "vehicle" (and to a lesser extent, its specific fraction of c).

E.g.: If a bowling ball were dropped onto one's right foot from a few inches up, and a needle were shot into one's left foot at a sufficient speed to match the bowling ball's total force (where F = ma), then the resulting energies involved would be equal, but the effects would differ greatly.

Edit: celtschk raised a specific point in the comment below, underscoring the specification that this event is "enough to kill life on earth if it had hit earth" (or similarly: "enough energy to destroy all life on Earth" in the question).

Object-configuration aside, if the event were sufficient to cause a 100% E.L.E. on Earth (had it hit Earth), then the result of hitting Luna would indeed have devastating effects for Earth.

• If Luna were fractured into large pieces in this event, then the immediate effects would likely include some significant portion of the mass hurtling out of orbit, and a similarly significant portion hitting Earth (whether in a glancing broadside blow, or fairly directly head-on). Neither case is liable to permit survival of much more than extremophile archezoa, if even that much (and assuming that Earth itself survived this event).

• If any in-falling pieces were insufficient to destroy the planet or cause essentially 100% extinction (and ignoring the obvious effects of a regular E.L.E. in itself), then we would be without a moon (though there would likely be debris orbiting for a very long time, possibly forming a ring). Tides would become greatly decreased, culture would suffer psychologically, the entire climate would be vastly altered (for how long, I hesitate to guess, but likely at least thousands of years at a bare minimum).

• The specification was "enough to kill life on earth if it had hit earth". I don't think at that point there would be much difference between needle and ball, as the relevant effect is not local. – celtschk Jul 19 '16 at 20:07
• This would be better if it were worded as a self contained answer rather than a response to a series of comments – Separatrix Jul 19 '16 at 20:47

You would not see it coming; just a huge splat when it arrives at the same time as any information about it. Such a splat would be a very bright light happening to quickly to see any detail.

The specific parameters are hitting the Moon at the terminator, so an extremely visible fireball will develop, and since we are talking about an RKKV, this will be a plasma at nuclear fireball energies. Without specific parameters of the RKKV's mass and velocity, it is hard to quantify things, but we can assume that the RKKV was designed to sterilize planet Earth, so it will be massively overpowered in relation to the Moon.

From the Atomic Rockets "Boom Table" , the minimal energy needed to kill life on Earth seems to range from 3.2 × 10^26J (blow Earth's Atmosphere into Space) to 1.5 × 10^30J, blast the Earth's crust into space. (Reducing the Earth to a pile of gravel or blasting the gravel out of spar orbit is a tad excessive in terms of energy expenditure).

While I haven't found the figure for the gravitational binding energy of the Moon, I would guess that once you get past "blow the Earth's Atmosphere into space" you are well on your way to destroying the Moon itself.

So the blinding fireball of plasma will either be propelling large pieces of the Moon at hypersonic velocity towards the Earth (resulting in a global shower of dinosaur killer asteroids and the resulting firestorms, Tsunamis, earthquakes etc.) or the blinding cloud of plasma will be engulfing the Earth, stripping away large portions of the atmosphere and boiling the oceans on the side of the Earth facing the Moon. With enough energy, the plasma and radiated energy could even affect Mars and Venus (as per the obligatory XKCD comic).

The millisecond after impact

So without quantifying things, an RKKV designed to destroy life on Earth will have more than enough energy to destroy the Moon and devastate the Earth at the same time.

It should also be taken into consideration that relativistic high-energy projectiles might give some of their speed to the target upon impact, which means that the orbit of the moon (or what will be left of the moon) could change. In the worst case, the moon would of course collide with the earth, but I don't think it would be THAT serious. Just a measurable change in orbit, maybe apoapsis or periapsis off by a couple thousand kilometers, a change in inclination, etc...

This would of course affect tides.

I believe Neal Stephenson gives a pretty lucid description of the process of Lunar decay after it is impacted by an unknown object moving at relativistic speeds in his novel "Seveneves".

Basically, the moon would break into several large chunks, common center of gravity wouldn't change all that much. These chunks would bang into each other, eventually grinding each other into finer and finer boulders and gravel. This smaller material's orbit, spread over a larger area, could possibly decay to the point of reentry. Such a large volume of fine material entering earth's atmosphere —aside from larger bolides acting like meteors, blasting the surface— would heat the atmosphere and boil the oceans... (Thucydides notes some of this, above, in his/her speculations.)

According to this sci-fi novel. It also seems quite plausible that some nuclear event would happen and the moon would just detonate like a very large nuclear device... the XKCD citations above describe that process, kinda.