The object was originally "fired" as a weapon used from space to hit planets.let's say it is a long cylinder with a very high density and it was accelerated at some point to 90% of C.

The missile ultimately missed its target and drifted into deep space at relativistic speeds. Eventually it makes its way to the Sol system and scores a direct hit on Jupiter (let's assume 90° from the ground).

I know some of the mass will burn up on atmospheric entry but the object is moving forward with the smallest profile and most of it should hit whatever serves as the surface.

I don't know how long or heavy the projectile should be, I'm just wondering if this is reasonably possible with this type of weapon. I'm looking to destroy Jupiter or at least remove a large portion of it's mass, blowing it into space. Is this remotely possible or would Jupiter just "swallow" the projectile? If Jupiter was blown to pieces, how would that affect the solar system as a whole?

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    $\begingroup$ since a larger than Jupiter object going at 90% C would satisfy this requirement you should choose an approximate size of projectile. Or, change it to what is the smallest size that would destroy jupiter. as it is there are too many variables to be able to judge a best answer. Additionally, what would destroy jupiter and what effect it would have on the solar system are two very different questions deserving their own posts. just my 2 cents $\endgroup$
    – IT Alex
    Jul 12 at 18:30
  • $\begingroup$ You may be interested in this question. Even though the Sun and Jupiter are very different, I would expect the result to be very similar. Your projectile is unlikely to penetrate very far into the Jupiter, and greater fractions of c don't help you. $\endgroup$
    – BMF
    Jul 12 at 18:30
  • $\begingroup$ Having a mass figure for the missile would help the calculation. You've already provided the velocity so with mass added it's possible to work out the amount of energy released on impact (in very round figures). $\endgroup$
    – Mon
    Jul 13 at 1:01
  • $\begingroup$ One question at a time please. $\endgroup$
    – John
    Jul 13 at 2:55
  • $\begingroup$ VTO so far objections to the question look like people assume we (or maybe those people) can answer the question or describe the situation for any specific situation. Guys if you can answer then do not be so stingy, do answer - would very much like to see any answer and downvote wrong and weak ones. HDE did a smart move considering situation around binding energy, and there are other smart moves, so as with binding energy answer can be improved. It hard to ask the question in specific way, so use the freedom provided to answer what u can answer here. It just 0.9c impactor against Jupiter. $\endgroup$
    – MolbOrg
    Jul 13 at 5:22

We recently had a question very similar to this about a relativistic asteroid impacting the Sun. I made the argument that the asteroid would not survive because the high speed would translate to quite a lot of ablation, as the intense drag forces in the photosphere tore it apart. Even if it penetrated to any reasonable depth, the high temperatures in the solar interior would further contribute to its demise; the Sun is simply big and massive and extremely hot.

Jupiter is a slightly different case, because it's smaller, less massive and cooler. It also has a much lower gravitational binding energy,$^{\dagger}$ which is $$U=\frac{3GM_J^2}{5R_J}\approx2.063\times10^{36}\text{ Joules}$$ You'd need to reach that energy with your projectile to rip the planet apart. ​Take 52 Europa, one of the largest asteroids in the Solar System, with a mass of roughly $2.26\times10^{19}$ kg. Accelerate it to 90% the speed of light. The energy of that asteroid will then be $$E=\frac{mc^2}{\sqrt{1-(v/c)^2}}\approx2.0619\times10^{36}\text{ Joules}$$ which is actually pretty close to the planet's binding energy! At the speed you list, it has a chance of disrupting Jupiter - assuming all of the kinetic energy goes into unbinding the planet.

(By the way, this is a lot of energy, as much energy as the Sun generates in 170 years. When thinking about how feasible it is to destroy Jupiter, keep this in mind!)

On the other hand, say that kinetic energy all goes into thermal energy. In that case, it would increase Jupiter's temperature by $$\Delta T\sim\frac{\mu m_pE}{M_Jk_B}$$ with $\mu$ the mean molecular mass, $m_p$ the mass of a proton and $k_B$ Boltzmann's constant. For $\mu=2$, I get an absurd mean temperature on the order of 100,000 Kelvin, which would make Jupiter substantially more luminous than the Sun despite its small size (though still too cool for nuclear fusion to set in). It would also break down molecules in the atmosphere and ionize atoms, leading to an object unlike any we know considering its mass.

The truth is likely somewhere in the middle; just where, I don't know for sure. Based on the above, my SWAG here for the scenario of a kinetic projectile like 52 Europa is that you'd see the following:

  • Extreme heating and subsequent expansion as the planet reaches a new hydrostatic equilibrium, now that the temperature increase has led to an increase in pressure. The atmosphere will be at least partially, if not fully, ionized.
  • In the case of a direct impact, the core would likely be disrupted to some extent, if not torn apart. This could contribute to the remains of the planet losing some of its gaseous envelope over time, largely the hydrogen and helium.
  • Asteroid resonances may disappear, changing the structure of the asteroid belt. The orbits of some trojan asteroids will certainly be disrupted.
  • Since Jupiter isn't in resonance with any planets, I don't think there will be other significant gravitational effects - although a hotter Jupiter would be problematic for Earth.

All of this will change if you change the mass of the projectile. A lower mass will not destroy Jupiter (as we'd have $E<U$); a higher mass would stand a better chance, although there are very few asteroids in the Solar System with the mass to do so, even traveling at 90% of the speed of light, and you'd clearly need to chuck an asteroid-like object at Jupiter to have a chance of destroying it.

$^{\dagger}$About five orders of magnitude lower than the Sun, for what it's worth.

  • $\begingroup$ Thank you so much, I see now that I'm going to have to blow apart a smaller planet. It's nice to know I was in the ballpark though. $\endgroup$
    – Leviathann
    Jul 12 at 19:31
  • $\begingroup$ Mean speed for hydrogen atoms(ions) at 100'000 K is around 62km/s, which above escape velocity 59.5km/s. So significant loss of mass is expected in heating scenario. This "new hydrostatic equilibrium" only for remnant of ex-jupiter. And be sure it will be a plasma ball with close to 100 percent ionisation of whole thing. I mean u need to multiply your SWAG by over 9000, lol $\endgroup$
    – MolbOrg
    Jul 12 at 19:35
  • $\begingroup$ @HDE 226868 If the temperature of Jupiter is raised so much it becomes as luminous as the Sun until it gradually cools off, life on Earth will find that its goose is cooked by the addiitonal heat. $\endgroup$ Jul 12 at 21:46
  • $\begingroup$ @M.A.Golding Yes, I did mention that. $\endgroup$
    – HDE 226868
    Jul 12 at 21:48
  • $\begingroup$ @HDE226868, Your answer makes me wonder whether Jupiter would also lose some moons in the process. $\endgroup$
    – user20568
    Jul 13 at 4:05

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