My science project
The Earth was built to last. It is a 4,550,000,000-year-old, 5,973,600,000,000,000,000,000-tonne ball of iron. It has taken more devastating asteroid hits in its lifetime than you've had hot dinners, and lo, it still orbits merrily. So my first piece of advice to you, dear would-be Earth-destroyer, is: do NOT think this will be easy.The page considers alternatives ranging from arranging for the Earth to be swallowed by a black hole to just waiting around five billion years for the Sun to swell up to a red giant and engulf the planet. Some are more practical than others. The "wait till the Sun goes red giant" plan is almost 100% guaranteed to work, but isn't very useful if you are in a hurry.
I actually looked into this once, a few years ago. The big obstacle to overcome is that the Earth's is held together pretty tightly by its own gravity. Imagine that we start to take the Earth apart. We dig up a piece of the crust and then accelerate it to escape velocity, flinging it into space. Then we dig up another piece and repeat. The biggest difficulty is launching the fragments fast enough to escape the Earth. That takes a lot of energy. In fact, this is going to take more energy than would be needed to melt the whole Earth, even if the inside of the Earth were not molten to begin with.
Here's the math. The energy we have to add to the Earth to overcome gravity and disperse its parts is called the Earth's gravitational binding energy. A fair estimate of this is GM2/R, where G is Newton's constant, M is the mass of the Earth, and R is the radius of the Earth. (The exact value depends on how the mass is distributed within the Earth, but this estimate is close enough to go on with.) Using tabulated values for the various factors, we come up with about 3.7 × 1032 Joules. Where the heck are we going to get 370 thousand million billion trillion Joules?
The best thought is nuclear energy, perhaps hydrogen fusion. We'd like to use a local source for the fuel, and the most obvious source of hydrogen is the oceans. So the question is whether there is enough hydrogen in the Earth's oceans to dismantle (pardon the pun) the Earth.
The total mass of the oceans is about 1.4 × 1021 kilograms, but of course only about 10% of this is hydrogen, the rest being oxygen and dissolved salts and stuff. When hydrogen is fused into helium, about 0.7% of the mass is converted to energy. That's a conversion of almost 1017 kg into energy. Using E = mc2 , we find that 8.8 × 1034 Joules are available from the fusion of hydrogen from the Earth's oceans. That is more than enough; indeed, that is enough energy to disassemble the Earth over 200 times.
Compare this to the energy available from solar energy. Sunlight has an intensity of about 1400 Watts per square meter, or about 1.8 × 1017 Watts over the area of the Earth. (We use the cross-section area for the Earth, of course, since that is the amount of sunlight that is actually intercepted by the planet.) We would need to use the Earth's solar input for about two trillion seconds to get enough energy to take the Earth apart -- about 66 million years. Plainly, fusion of oceanic hydrogen is the quicker energy source!
As an aside, I note that, if we somehow lost the Sun, the hydrogen in the oceans would provide us with an alternative way to keep the Earth warm. It would take about 90 billion kilograms of water per year to generate the same amount of energy that the Sun provides, but that really isn't so bad. It's a tiny amount, comparatively: less than one micron of water depth over the whole ocean, with a correspondingly tiny increase in atmospheric oxygen and helium. I do not expect the Sun to become unavailable any time soon, of course, but it is nice to know that we have a potential back-up system, just in case.
Why do physicists like me find such playful calculations so amusing? This is a kind of humor that is hard to explain to non-science types. To them, working a physics problem could not possibly be a source of amusement. Well, I guess you either get it or you don't. Do economists, say, have the same sort of fun with their own "dismal science"? (OK, maybe they do.) In any case, at the moment I can't help but grin when I learn that the Earth's oceans represent an energy source capable of (a) replacing the Sun's energy input for several billion years, or (b) taking the Earth completely apart, as required. (The details of either enterprise, of course, are left as an exercise for the student.)