How big of a nuke would be needed to disperse jupiter?

I read something about Jupiter then about nukes. Assuming that the bigger a bomb gets the more powerful it gets, then how many miles/Kilometers long would the Nuke need to be? Please be serious.

 Short answer: You’d need about 10 quintillion nukes, which is 4x the mass of the moon, to destroy Jupiter. That, or, a pile of TNT approximately equal to the mass of the sun should do the trick.

Long answer:

Please be serious.

I make no promises.

The gravitational binding energy of a spherical mass is given as:

Potential energy = 3 x (Gravitational Constant) x (Mass)^2 / 5 x (Planetary Radius) 

So, to a first approximation, we need to add at least this much energy to the center of Jupiter to blow it apart. Of course, no bomb will be perfectly efficient because a lot of energy will likely get radiated as heat so we’ll probably need considerably more energy than this… but it’s a good first approximation.

Anyway, the mass of Jupiter is about 2×10²⁷ kilograms, which is about a thousandth of the sun. The radius of Jupiter is about 70000 km, which is about a quarter of the distance from the earth to the moon, so the total binding energy is about 2×10³⁶ Joules, and Wolfram actually knows the answer already without me having to plug in numbers.

For reference, that’s comparable to the total energy output of the sun over a century. But that’s boring, you didn’t want the sun to unbind Jupiter, you wanted nukes to do the heavy lifting.

As is tradition, we use the Tsar Bomba. The Tsar Bomba produced the largest manmade nuclear detonation, releasing 2×10¹⁷ Joules of energy. We’d need close to 10¹⁹ of these bombs. This number is so big that I don’t even know the word for it off the top of my head- I had to look it up to make sure I had it right. I’d be content to call it a fucktillion, but for the sake of accuracy I should say that this is equal to “10 quintillion” or “ten billion billion.” Even if each of these nukes cost 1 American penny, with the approximately $100 trillion in equivalent cash on earth, you could only buy 1/1000th the number of nukes you’d need.

Anyway, Wikipedia tells me the Tsar Bomba had a mass of 27 tons, so this pile of nukes would have a mass of about 2×10²³ kg. This is about 4x the mass of the moon. Let that sink in. A pile of nukes 4x more massive than the moon is needed to destroy Jupiter.

Another fun unit is TNT equivalents- for the same blast yield as the nuke, how much TNT do you need? The Tsar Bomba was equivalent to about 50 megatons of TNT. “Megaton” being millions of tons. For 2×10¹⁹ piles of TNT,you’d need about 10³⁰ kg. That’s half the mass of the sun.

Crazy, right? That means that even if you made a Jupiter out of TNT and you blew it up, there wouldn’t be enough energy from the explosion to blow the planet apart- it would puff up, but gravity would still be able to pull it back together. If anyone can recommend a good Minecraft mod where I can simulate this, I’d be grateful.

You can actually use this info about the binding energy, along with the energy and mass density of TNT, to calculate the maximum mass for a pile of TNT that will be able to gravitationally unbind itself. For example, a single stick of dynamite should be able to blow itself apart without gravity pulling it back together, but a solar mass worth won’t be able to overcome gravity. Anyway, it turns out the maximum mass of self-unbinding TNT is equal to about 10²¹ kg. This is a little less than the mass of Pluto, so handle with care.

Let’s make it more interesting. Extrapolating from these numbers, and given that 1g of antimatter produces 180 terajoules of energy when mixed with a corresponding amount of matter, you’d need about 10¹⁶ tonnes of antimatter. That corresponds roughly to an asteroid 100km across made entirely of antimatter.

But this begs the question, if we destroyed one of the planets in our solar system, what effects would it have on our planet? Is it possible to move Earth off its path?

It really depends on which planet you choose to destroy. Jupiter could possibly have the greatest effect on the inner solar system for two reasons:

• Jupiter shepherds the asteroid belt. Without Jupiter the belt could potentially grow unstable and that might increase the amount of debris in the inner solar system.
• Jupiter is an asteroid and comet sponge, absorbing many “rogue” chunks of rock from entering the inner solar system.

So basically.. Jupiter is indestructible. Well, unless it collides with a sun-sized object.

You could probably scoop it up a bit at a time. It would just take a while. There’s a hypothetical megaengineering project, called a Jupiter brain, that would involve taking Jupiter (or another giant planet) apart and turning its useful mass into a planet-sized supercomputer. That could actually be feasible for an advanced technological civilization.