Mysterious Agent Blows Up Moon: Can Earth Survive?

[Sherwood Botsford]

Story in brief: An unknown agent blows up the moon, initially into 7 major pieces and a bunch of little ones. The pieces are gravitational bound, but collisions between the pieces continues the break up process.

Stephanson postulates that the number of pieces reaching the Earth's atmosphere will increase to the point that in 2 years Earth will experience a 'white sky' from re-entering rocks, which will burn off the surface of the planet, and that this will last for several thousand years.

I don't understand how this is possible.

I know that in elastic collisions a small object can come away with a larger velocity. The classic experiment is to drop a tennis ball 1" apart from a basketball at the same time. The basketball coming up meets the tennis ball coming down, and the tennis ball leaps away at about twice the speed relative to the floor.

But collisions are not going to be elastic. Much of the energy will be consumed breaking big rocks into little rocks, and relative speeds are going to be low. (The description has the 7 major chunks being indistinct in a cloud of debris a week later, and being a patch several times the diameter of the full moon.)

To burn off the surface of the earth, you need dump an appreciable fraction of the amount of energy the Earth gets from solar radiation. The moon is 1/80 of the mass of the earth. Positing 5000 years of bombardment we are talking about 1/400,000 of the mass of the moon per year, if the entire moon came down. This would be a planet wrecker: At 22 billion cubic km 1/400,000 is still a lot of rock.

But from a gravitaionally bound cloud of rocks, what would be the ejection rate of mass? Given the initial descriptions, I figure that most of the mass would recollect into a new moon.

 

[willem2]

To get the same power as the sun on Earth (5*10^17 W) by collisions, you need 1.2 * 10^17 kg/year. In 5000 years, that's 6*10^20 kg. Only 0.83% of the mass of the moon, so this seems possible. If there are 7 major pieces in orbits around each other, smaller rocks can easily pick up enough energy to escape by slingshot manoeuvers. They would still orbit the Earth in a roughly moonsize orbits. Interactions with the bulk of the mass of the moon will then likely make those crash on the Earth or the moon eventually.
It also seems likely that an explosion that breaks up the moon will put some of the mass of the moon past moon escape velocity directly, although much of this might also escape the earth, the remainder that remains in Earth orbit might still be enough.
I

 

[Rubidium_71]

Couldn't resist posting this -

 

[stefan r]

Should this be in the fiction forum?

...

Stephanson postulates that the number of pieces reaching the Earth's atmosphere will increase to the point that in 2 years Earth will experience a 'white sky' from re-entering rocks, which will burn off the surface of the planet, and that this will last for several thousand years.
...
But from a gravitaionally bound cloud of rocks, what would be the ejection rate of mass? Given the initial descriptions, I figure that most of the mass would recollect into a new moon.

Dust will scatter sunlight. Light reaching your eyes would originate from all angles. The Sun's region would be brighter than other regions but dimmer than it is now.

Meteors create their own light and leave ion trails.

A lot of dust in the upper atmosphere could create a "nuclear" winter effect. The surface wind would be blowing from poles to equator.

 

[ensign_nemo]

If the moon explodes then Earth would be hit by enough debris to sterilize it almost immediately.

There wouldn't be anybody left alive after a very short period of time.

That might be boring fiction but if something shatters the moon then it's definitely going to send a fair amount of debris toward Earth.

 

[rootone]

An asteroid big enough to shatter the Moon in a collision would have to be a good percentage of Moon sized itself.
If there were such an asteroid inbound towards the Earth-Moon system it would more likely hit Earth directly rather than the Moon.
Earth is considerably bigger and has a lot more gravity than the Moon does.
I think the most likely scenario though is it would not hit Either, but would eventually settle into a stable orbit as Earths second Moon.
I can't think of any other situation which could potentially demolish the Moon/
I doubt even if the most powerful nukes we have could do it.

 

[Sherwood Botsford]

Willem2 has some good points. But I'm not convinced either by the elasticity of collision, or the efficacy of sling shotting. Indeed, the initial time would be the dangerous one, when there is a reasonable chance of one of the large chunks losing enough momentum to hit the earth.

In ore processing some typical numbers for a ball mill -- pebbles to powder 1 hp of motor per ton of rock per day. Powder size is .05 mm.
So that's 3600 seconds * 745 W / 1000 kg. = 2700 J/kg. This corresponds to a speed of 73 m/s, a fairly pedestrian pace compared to orbital velocities.

An example of the weakness of rock: Curling stones are made of granite. But they have a steel band on them. The band distributes the force of impact to the whole stone. Another example: I rolled an 18" pink sandstone boulder off the edge of the Mugallon rim, a 900 plus foot cliff. We had time go get on our bellies to watch it hit. Seconds go by. We lose track of it. Suddenly: A pink dot on the dark basalt. A bit over a second later CRACK!

The flip side of this: Not a huge amount of energy is lost doing the grinding. On the other hand, as breakup proceeds, the effective total cross section increases, so impacts increase, very rapidly. As size of particle decreases, the ratio of strength to the strain of impact increases. So at some small size, collisions are going to become elastic.

At some point too, the particle size gets small enough that particles are going to be affected by the combination of light pressure and solar wind. Not sure what size this becomes significant. Might be pretty.

When I first read about Roche's limit, the notion was that rock had insignificant strength compared to tidal forces. This after all was why planets were round. Most of the major asteroids are resemble turnips and onions more than potatoes or carrots.

This would be a difficult problem to simulate. But we have examples:

* Once we have a ring structure, it is at least metastable. Saturn doesn't suffer from white sky.

* At the stage of having a hundreds of thousands of rocks, would it be comparable to a globular cluster? We can look at those and check for objects that were ejected from the cluster.

An asteroid big enough to shatter the Moon in a collision would have to be a good percentage of Moon sized itself.
If there were such an asteroid inbound towards the Earth-Moon system it would more likely hit Earth directly rather than the Moon.
Earth is considerably bigger and has a lot more gravity than the Moon does.
I think the most likely scenario though is it would not hit Either, but would eventually settle into a stable orbit as Earths second Moon.
I can't think of any other situation which could potentially demolish the Moon/
I doubt even if the most powerful nukes we have could do it.

Agreed. In the novel, it was done by an unknown agent. The moon was not shattered, but left in 7 large chunks plus some smaller debris. Reference is made early in the book that the pieces were mutually orbiting, but at a distance from each other that it was a week before the first collision that turned 7 into 8 chunks.

I find this implausible too. The moon is some 3500 km in diameter, which makes each chunk several times larger than Ceres, so they would self round from gravitation.

 

[Sherwood Botsford]

Just had another thought. Does it matter where in the atmosphere they transfer their energy? E.g. If they are small and burn up at 60 miles elevation, then far more of the energy radiates directly out to space. (At least half). Some air is ionized, but at this elevation lots of ions anyway. If recombining ions all do so at visible wavelengths, then transfer to the surface is efficient for photons aimed that way. If the recombination occurs at far IR wavelengths, then the greenhouse effect helps in reverse. In either case, if most of the energy is turned to radiation at high elevation, half of it goes into empty space.

Smaller particles decelerate faster, with the resulting energy dump at higher altitudes.

 

[stefan r]

In either case, if most of the energy is turned to radiation at high elevation, half of it goes into empty space.

Smaller particles decelerate faster, with the resulting energy dump at higher altitudes.

Small particles at high altitudes stay in the atmosphere for a long time. A 100 micron dust layer can block light. A lot of energy from new dust would be adsorbed or reflected by older dust.
Still completely trashes the environment on earth.

 

[Sherwood Botsford]

Followed up my own suggestion and did some reading on globular clusters, figuring that they were the closest equivalent to a swarm of rocks.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253893/

Which seems like a very odd place to find such an article. National Institute of Health?

* The crossing time: Time it takes to go from one side of the cluster to another.

* The relaxation time == average time for a star's velocity to be randomized. That is, for the star's original velocity to be altered by about that velocity. This is approximately equal to Tcross * 0.1N / ln(N) N is the number of stars.

* Mean square escape velocity is 4W/M where W is the total gravitational potential energy and M is the total mass. This works out to being about 2 times the average velocity.

* If speeds are distributed with a maxwellian distribution roughly 7.4 * 10^-3 or about 1/136 of them have a velocity over twice the RMS mean at any given time.

I question this assumption. I would expect some sort of equipartition of energy to go on so that the average kinetic energy would be the same. So small objects would be fast moving objects and would evaporate from the cloud rapdily.

So this answered one of my objections. Such a cluster will eject material quite efficiently.
Worse. We can't choose a simple ratio of cross sections of Earth's diameter to the diameter of the moon's orbit. Rocks ejected from the lunar cloud are likely to go into an orbit around the earth, giving them more chances to be further perturbed and hit the earth, or the orbital shelters. Even if in orbits that don't intersect the Earth, the region is going to be troublesome for space travel.

Given that most of the material will be very small, I think that Steffan R is correct. We end up with a prolonged nuclear winter instead of cooking the planet. While this is more favourable for the survival of life (Tardigrades forever!) it does not bode well for humanity.