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Pretty self explanatory hypothetical. I realize this is probably an impossibility and maybe it'd be more likely to be hit by a small black hole or primordial black hole. I'm just curious, because we always talk about how much a teaspoon of neutronium would weigh on earth.

Qmechanic
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Al R
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2 Answers2

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The teaspoon of neutronium would have a mass of about $10^{12}$ kg.

Due to it's small size (and area), the pressure caused by the impact would be very high, so it's likely to plough straight through the earth and out the other side.

It depends on the velocity, but things coming from space are usually moving fast.

As the earth has a mass of $6\times 10^{24}$ kg the orbit of the earth wouldn't be changed much.

John Hunter
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  • The going through the earth suggestion hasn't been checked by careful calculations, if anyone wants to do anything on this it would be interesting to see if it goes through or if the impact spreads out... – John Hunter Dec 15 '21 at 09:46
  • Would you even need an impact? You might be able to just rest it gently on the ground. – DKNguyen Dec 15 '21 at 15:25
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    I don't think it will simply plough through the Earth. The pressure deep inside a neutron star is on the order of $10^{32}$ Pa. Without that pressure, a ~1 cm radius ball of neutronium will expand to ~1 km radius rather quickly. ;) (The speed of sound in a neutron star is relativistic). – PM 2Ring Dec 15 '21 at 16:49
  • DKNguyen yes, maybe so, then it might just reach the other side - think we need more details from the questioner about the speed and whether as PM 2Ring said, whether they meant that it could expand – John Hunter Dec 15 '21 at 17:37
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You haven't specified the speed of impact but it is reasonable to assume that it wouldn't be much less than the escape velocity of the Earth - about 25,000mph. I've just done a calculation of the kinetic energy based on 5 cubic centimetres and the result wouldn't be good for the nearby inhabitants. I make it about $3.1$x$10^{19}$ joules, which is equivalent to a 7400 megaton nuclear explosion. i.e. about 150 times the most powerful bomb ever detonated (the Tsar Bomb). However, the impact of the meteorite that was responsible for the extinction of the dinosaurs is believed to have been equivalent to 100 million Tsar Bombs.

Rob Tristram
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  • The energy released will be 1000 times that of the asteroid that finished off the dinosaurs. You are out by nearly 10 orders of magnitude and the speed of impact is almost irrelevant. – ProfRob Dec 15 '21 at 20:30
  • https://physics.stackexchange.com/questions/10052/what-would-happen-to-a-teaspoon-of-neutron-star-material-if-released-on-earth?noredirect=1&lq=1 – ProfRob Dec 15 '21 at 21:47
  • Density of neutronuim = $10^{14}g/cm^3$ 1 tsp = $5cm^3$ Mass of neutronium = $5$x$10^{11}kg$ Velocity at impact = 11,200m/s Kinetic energy at impact = $5$x$10^{11}$ x $11200^2/2 = 3.14$x$10^{19}J$ I was out by a factor of 10 to begin with - will edit - but not with the final result.

    1 megaton = $4.18$x$10^{15}J$ Therefore Impact energy = $3.14$x$10^{19}$/$4.18$x$10^{15} = 7500MT 7500/50 = 150 Tsar Bombs

    Impact at Chicxulub crater: "For comparison, this is ~100 million times the energy released by the Tsar Bomba" https://en.wikipedia.org/wiki/Chicxulub_crater

    Correct, I believe.

     – Rob Tristram Dec 15 '21 at 21:55
  • Incorrect, since you have not considered the internal energy of neutron star matter. – ProfRob Dec 15 '21 at 21:59
  • I put my hands up, but I want to say in my defence that I was not unaware of what neutron star matter was - maintained by immense gravity - I just seem to have forgotten that in my zeal to calculate the megatonnage due to the KE.

    However, it should be pointed out that the phrase in the question "crashed through the Earth's atmosphere" has been ignored in the referenced answer. That would require confinement of the matter by some magical force for the period of its re-entry and then its release it when in contact with the Earth's surface. And what if it wasn't released?

     – Rob Tristram Dec 17 '21 at 15:51
  • Indeed. Magical. And thus an answer could have been - it can't happen. – ProfRob Dec 17 '21 at 17:34