How can I destroy a gas giant planet?

While ckersch's answer is correct on the energy needed there's a deeper issue involved here that I think you are missing:

The main part of the energy needed to destroy a planet is the energy needed to push the components to escape velocity. For the back of the envelope calculations people are doing on here the nature of the planet doesn't matter.

There are two basic sources of inaccuracy in the calculations: They ignore the chemical binding energy and they assume each bit of mass takes the same energy to boost away.

The first simply can't be calculated as it's based on an unknown value. The smaller the bits you turn the planet into the more energy that is going to be needed (and remember even gas giants have a rocky core, they still have some chemical binding energy.)

The second is a much bigger source of error. The inside of a spherical shell is in zero gravity. To correctly calculate the gravitational binding energy you have to blow off a series of infinitely thin shells, recalculating the escape velocity after each one. In practice this will be impossible for anything other than Earth as you need a density profile of the planet.

The escape velocity of a sphere is $$\sqrt{\frac{2GM}{R}}$$ thus the simple answer is $$\sqrt{\frac{2GM}{R}}M$$ but the actual gravitational binding energy of a uniform sphere is $$\frac{3GM^2}{5R}$$ Note that even here how much you break it up is a big deal--that's 80% more than the energy to split it into two parts receding at escape velocity. I won't even dream of tacking the binding energy of a non-uniform sphere.

posted almost 10 years ago

Loren Pechtel‭

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Blowing Saturn up would be hard.

Saturn has a mass of $568.3\times 10^{24}$ kg, or about 95 times the mass of Earth. To blow up Saturn, i.e. to place some sort of unimaginably huge bomb in its center and vaporize it, you'd have to energize all or most of that mass to escape velocity, otherwise it would just reform out of the cloud of gasses. The escape velocity of Saturn is 35.5 km/s, so this would take $1/2 \times 35,500^2 \times 568.3 \times 10^{24} = 3.6 \times 10^{35}$ Joules of energy.

For reference, this is the amount of energy the sun produces in thirty years.

Burning up all of the hydrogen also wouldn't work. You'd need to bring enough oxidizer to react with all of that hydrogen, which would weight 8 times as much as the hydrogen did in the first place. Then, once you lit it, the gas wouldn't have enough energy to escape into space, so all you'd really accomplish would be producing lots and lots of water.

So how do we destroy Saturn?

My first though was to toss a small star or black hole at it, but flying one over would probably take more energy than just blowing Saturn up.

Instead, let's push Saturn into Jupiter. The energy required is equal to the difference between the starting orbit for Saturn and its finishing orbit. (We'll move Saturn instead of Jupiter because it's a bit smaller) This is given by the equation $E = \frac{-GMm}{2a}$, where $GM$ is the standard gravitational parameter (of the sun, in this case), $m$ is Saturn's mass, and $a$ is the semi-major axis. The orbital energy of Saturn in Saturn's orbit is $-5.3 \times 10^{28}$. (The convention with orbital energies is that the planet has zero energy at an infinite distance from the sun.) The energy in Jupiter's orbit will be $-9.7 \times 10^{28}$, giving a total energy needed to throw Saturn at Jupiter of $4.4 \times 10^{28}$ joules, which, while enormous, is several orders of magnitude less than what we'd need to blow it up outright.

(Note that the energy change is negative, but assuming that we use a Hohmann transfer orbit, we'll be burning the same amount of energy in our velocity changes to decrease our orbital radius as we would need to increase it. Maybe. I think. Orbital mechanics was 5 years ago, now.)

posted almost 10 years ago

ckersch‭

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