A 1 kilometre wide sphere of U-235 appears in an orbit around our planet. What happens?

Question

Let's suppose that after seeing aliens get portrayed negatively in science fiction and wishing to end the discrimination, the ancient H'andh'wh'a'vians decide to destroy Earth and humanity.

As they are a Tier-U-uber-civilization, they decide to just spawn a sphere of Uranium-235 in a circular equatorial orbit with a sea level altitude of 400 kilometers.

The diameter of the sphere is 1000m. Apart from U-235, there are no other materials or impurities at T=0. You can assume that any atoms that would be displaced by the sphere are removed prior to its creation.

• What happens?
• Does the explosion occur immediately, or only at impact/atmospheric entry?
• How long does it take for orbital decay to put the sphere out of orbit?
• How bad is the explosion and what effects does it have? Is there any chance for survival? Is the Planet's orbit altered significantly?

Answer 1

Normally, only the innermost kilogram of uranium in an implosion-type bomb actually undergoes fission (and only 0.6 to about 5g of mass are ultimately converted to energy - the sources don't agree on this), because the explosion itself vaporizes and blows apart the rest and the fission cannot proceed further. This, by the way, was the main limit to the size of fission devices, that led Sakharov, Ulam et al. to design fusion devices.

In this case, though, practically the whole mass of uranium undergoes fission within a millisecond, while the outer shell (while still exploding) acts as a tamper. Only a very thin layer will neither undergo fission nor provide inertial confinement. Immediately after, the enormous neutron flux will trigger fission in that thin layer too.

At the same time, the neutron density will be enough to achieve a very high burn everywhere inside the sphere. So, while Little Boy had an efficiency of about 1.4%, and we can expect a fission efficiency of 50% (same source) due to the size, the actual energy efficiency will be much higher because the reaction will proceed further. A rough (probably incorrect) estimate based on the hypothesis that all the byproducts will be made up of the lowest (most "burnt") isotopes from the Hiroshima explosion tells us that the per-mass energy release should be about twenty times higher. And the mass of the sphere is around 9,948,368,333,000 higher than the fissioned mass at Hiroshima; we can then estimate an energy release to the tune of three billion megatons.

I wouldn't be surprised in the least if the radiation density at the center of the fireball allowed photodisintegration (photo-fission) and further increased the energy release (or maybe the reaction would find an equilibrium between photofission and nucleosynthesis, which is endothermic).

There is no need to calculate the exact magnitude of the explosion: it would not be enough to vaporize the Earth, but the radiative shock would scorch the target hemisphere and supply enough secondary activation to thoroughly poison the whole atmosphere as well as the oceans, as if the primary onslaught weren't enough.

The atmospheric blast reaches the other side of the planet after about sixteen hours - actually way less than that due to the speed of sound being higher in the high atmosphere - and increases constantly for at least eight hours; but the havoc it causes is probably nothing compared to the reentry of the incandescent, radioactive tephra from ground zero. Oh, the storm winds are radioactive too.

Primary concussion should be more than enough to trigger most existent fault lines, and seismic waves travel faster than sound in air; so for those countries that did not see the blast aurora, the first hint something went very, very wrong (apart from communications gone awry and possibly a sudden "sour, metallic taste in the mouth") might be a series of catastrophic earthquakes and volcanic eruptions.

Also, atmospheric pressure will finally stabilize to much lower value, possibly all the way to half of the former total, due to the gases being ionized and stripped off the Earth. In the worst scenario, oxygen partial pressure goes from 21% to about 11-12%, below the level sustaining current terrestrial life. I'm uncertain whether to count oxidation and burning - it might well be the case that there is not very much left to actually burn. If there is, then the oxygen goes still lower, and CO2 contents goes up.

Plus, the firestorm triggers the grandfather of all nuclear winters. Photosynthesis stops on the whole surface, probably for several years.

Plus the neutrino flux might supply enough inverse-beta decay to sterilize the whole planet, both hemispheres at once, or at least ensure death by cancer to all superior organisms.

Deinococcus radiodurans might yet survive.

Nothing else will.

Answer 2

T = 0.0000000000 seconds : The Sphere appears.

T + 0.0000000001 seconds: The Sphere disappears.
some...minor... light flash may be observed shortly thereafter, as the planet is vaporized.

Supporting numbers: sphere:
1000m diameter.
Radius 500m
volume 5.24e8 m3 total content = 5.24e14 cm3

Uranium-235:
Density 19.1 grams/cm3 Molar mass 235.0 Molar volume 12.3cm3

thus sphere = 42601626016260 moles (10.011 billion tonnes)

With so much more than critical mass, we can assume 100.0% fission. (there may actually be enough neutron flux to facilitate trans-uranic nucleosynthesis, similar to what occurs inside a supernova)

Energy released per mole of U235 fissioning: 1.954e10 J
Energy released by whole sphere fissioning: 8.3e26 J
Gravitational binding energy of planet Earth: 2.0e32 J

The explosion is not nearly enough to actually blow up the planet, it merely toasts it gently to a white-hot (radioactive, due to the neutron flux) cinder.

Ok, Maths fixed. The explosion is about 4 billion times bigger than the Tzar Bomba.
Still not enough to disrupt the whole planet, barely enough (if it was all captured, which it definitely won't be!), to raise the whole planet's temperature by about 1 kelvin. But ample to turn the whole hemisphere under the sphere into a kilometers-deep blast zone, and rip off every trace of atmosphere on that side of the planet.

Answer 3

I'm going to guess at it. I can't do calculations, so this is kind of a broad brush sense of some effects that might happen. In no special order:

• The sphere fissions. It fissions everywhere, the outside acting as others said, as a tamper even while detonating.

• The fissioning process leads to inward and outward directed pressures.

• The inward pressures, like in an H bomb, both tamper and contain, and for a small time create incredible pressure. Novel nuclear processes will probably arise. Photodisintegration was mentioned, that's one of those. Reactions will occur far longer and more completely than in A bombs which only typically detonate a small percentage of their uranium. The neutron flux can't escape without reacting, so even as a fission reaction it's far more complete - probably could be near total for much of it(?). (That doesnt mean total matter to energy, just very high or near total U235 fissioning, to be clear). The nuclear reaction byproducts also can't easily escape, except neutrinos. We know about neutrons and chain reactions, but expect other byproducts to be unable to escape as in a small A bomb, and they will contribute to increased or novel reactions too.

• The outward pressure may or may not cause the outer surface to shatter into fine dust, before being absorbed into the huge fireball. Bear in mind a small sphere a few cm, can fission, so anything more than a few cm from the surface will be close enough to enough uranium to almost instantly do so. Not much will be close enough to the surface to be blasted apart as dust before fission is.possible. The question is, will the reaction be so violent and contained that almost all uranium engages in some nuclear process, or will a fair bit of it be left as-is but as almost atomic dust? In a way it doesn't matter, because even the uranium that fissions will ultimately result in final byproducts that fission less easily or not at all, so expect a huge cloud of all kinds of interesting atoms and elemental isotopes. Many highly toxic or reladioactive. I don't know what proportion of mass ultimately ends up as energy., or the nature and division of byproducts. That's crucial. But takes some supercomputer modelling on this scale.

• We pan back a bit. The explosion sends heat, radiation, and general blast in all directions. Directly towards the atmosphere, away, and in retrograde orbit, among others.

• The blast and heat hit first, directly below and for much of the hemisphere facing the explosion. I don't know exactly how that plays out because a lot depends what momentum the particles and energy have, and that I can't tell. Probably huge, even though individually, microscopically small. Bear in mind energy has momentum and a heating/expansion effect, and a kilometer sphere even after very high levels of matter to energy conversion has a hell of a lot of matter left in it. The dinosaur killing asteroid was much larger but much slower moving perhaps. I suspect momentum and pressure would be due to radiation and heating/expansion effects not due to solid debris at high speed. But then again nuclear blasts we know of, all happened in dense air that (like the WW2 Dambusters bombs) added resistance and great momentum to the blast. This is happening some 350-380 km from any dense air, so the shock wave though huge spreads out to a sphere almost 400 times as large as it began, and perhaps dissipates considerably, before it can even begin to add any significant air to its blast momentum. Even then its many km to the ground.

• Either way, the atmosphere is not only impacted but heated and expanded, the heat is trapped, and everything simultaneously goes incandescent hot, and expands - and this adds hugely to the blast, which cirkces the world many many times. Turbulence, self interactions and storms are also colossal. I can't say how big earthquakes are. The heating effect magnifies momentum massively but how much of that translates into the ground or sea, I can't say. Assume big, for some value of "big".

• The sphere was in orbit. So on average, its fireball and debris still has some orbital bias. It's a huge expanding nuclear sphere whose centre is still in a 400km orbit, which means it circles the earth at about 7.57 km/sec and completes an orbit every 92 minutes. Any atomic scale dust and matter trails in its path, both blasted into and settling into the upper then lower atmosphere, and gradually spreading out to be a shell or ring around the planet most likely. Outer atmosphere friction and interactions mean the "tail" grows and it develops a thick ring like style more than a simple expanding sphere. Interactions with the earths magnetic field also influence its distribution and how.it lands. I don't know how long the fireball is ongoing, but if its more than trivial, then the hemisphere it detonated above is not the only place its exploding above or radiating into, either.

• Even when the reactions end, we need to consider the final temperature and distribution of the matter left. If we have dust at a million degrees circling and taking time to cool (I dont know what figures are sensible) or a superheated ring or huge growing cloud, we have further consequences of that, until it's cooled somewhat.

• As a byproduct, the earths ozone layer and its van Allen belts, protecting it from the vicious solar climate and radiation, are both probably badly screwed, too.

• Does the earth survive? Probably. No.idea how deep the changes go. The energy release and the amount that reaches earth heats and scours it, but I intuitively suspect isn't enough to unbind or fundamentally split it, maybe they don't go too deep at all comparatively??? After all, earth is 8000 km across, the closest solid surface is 400km away (although to an extent the atmosphere may act as if solid in the moment of explosion due to the forces unleashed), and eartjs volime is 8000^3 = 500 billion x the orbiting sphere's, and that's a hell of a lot to unbind even for a 1km sphere of pure fissioning nastiness... and most of earths mass is shielded by the ablation and the brunt of impact taken by the outer few km.