Why would someone ever want to do something like that? Well considering you're reading this article I'm sure you have a pretty good idea. If not, consider this list of hastily put together reasons: Why not?; Because it's there; For science!; 
To build a new intergalactic highway; To make a point (mad scientists will love this one); etc.
 
But destroying the Earth wouldn't be as easy as you might think. Sure, wiping out life is relatively easy, but not nearly as dramatic and visually pleasing as destroying the planet itself. Note however, that these methods do not guarantee the extinction of humankind, as the bastards are tricky and resourceful. Nor is this a guide for those wanting to annihilate everything from 
single-celled life upwards, render Earth uninhabitable or simply conquer
 it.
And before you say nukes, I'd like to make it really clear we don't have enough of them to completely destroy the earth. We might be able to dent it...maybe
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| No, they do not colour-code the mushroom clouds by country | 
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1. Annihilation with an equal amount of antimatter
- Antimatter - the most explosive substance possible - can be 
manufactured in small quantities using any large particle accelerator, 
but this will take preposterous amounts of time to produce the required 
amounts. If you can create the appropriate machinery, it may be possible
 to find or scrape together an approximately Earth-sized chunk of rock 
and simply to "flip" it all through a fourth spacial dimension, turning 
it all to antimatter at once.
 
- Method: Once you've generated your antimatter, probably in 
space, just launch it en masse towards Earth. The resulting release of 
energy (obeying Einstein's famous mass-energy equation, E=mc2) is equivalent to the amount the Sun outputs in some 89 million years.
 Alternatively, if your matter-flipping machinery is a little more 
flexible, turn half the Earth into antimatter (say, the Western 
Hemisphere) and watch the fireworks.  
 
 
2. Using a microscopic black hole
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| Where do black holes come from? | 
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- Note that black holes are not eternal, they evaporate due to Hawking 
radiation. For your average black hole this takes an unimaginable amount
 of time, but for really small ones it could happen almost 
instantaneously, as evaporation time is dependent on mass. Therefore 
your microscopic black hole must have greater than a certain threshold 
mass, roughly equal to the mass of Mount Everest.
 
- Creating a microscopic black hole is tricky, since one needs a 
reasonable amount of neutronium, but may possibly be achievable by 
jamming large numbers of atomic nuclei together until they stick. This 
is left as an exercise to the reader.
 
- Method: simply place your black hole on the surface of the 
Earth and wait. Black holes are of such high density that they pass 
through ordinary matter like a stone through the air. The black hole 
will plummet through the ground, eating its way to the centre of the 
Earth and all the way through to the other side: then, it'll oscillate 
back, over and over like a matter-absorbing pendulum. Eventually it will
 come to rest at the core, having absorbed enough matter to slow it 
down. Then you just need to wait, while it sits and consumes matter 
until the whole Earth is gone.
 

 
 
3. Blowing it up 
- You will need: 25,000,000,000,000 tonnes of antimatter or the equivalent.
 
- Method: This method involves detonating a bomb so big that it blasts the Earth to pieces.
 
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| Not an infographic, but how can you not like it? | 
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- This, to say the least, requires a big bomb. All the explosives 
mankind has ever created, nuclear or non-, gathered together and 
detonated simultaneously, would make a significant crater and wreck the 
planet's ecosystem, but barely scratch the surface of the planet. There 
is evidence that in the past, asteroids have hit the Earth with the 
explosive yield of five billion Hiroshima bombs - and such evidence is difficult to find.
 It is, in short, insanely difficult to significantly alter the Earth's 
structure with explosives. This is not to mention the gravity problem. 
Just because you blasted the Earth apart doesn't mean you blasted it 
apart for good. If you don't blast it hard enough, the pieces will fall 
back together again under mutual gravitational attraction, and Earth, 
like the liquid metal Terminator, will reform from its shattered shards.
 You have to blow the Earth up hard enough to overcome that attraction.
 
 
4. Deconstructing it piece by piece
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| Just so you know what we're trying to blow up | 
- You will need: a mass driver. A mass driver is a sort of over-sized electromagnetic railgun, which was once proposed as a way of 
getting mined materials back from the Moon to Earth - basically, you 
just load it into the driver and fire it upwards in roughly the right 
direction. Your design should be powerful enough to hit escape velocity 
of 11 kilometers per second.
 
- At a million tonnes of mass driven out of the Earth's gravity well 
per second, this would take 189,000,000 years. One mass driver would 
suffice, but ideally, lots (i.e. trillions) would be employed 
simultaneously. Alternatively you could use space elevators or 
conventional rockets.
 
- Method: Basically, what we're going to do here is dig up the 
Earth, a big chunk at a time, and boost the whole lot of it into orbit. 
Yes. All six sextillion tonnes of it.
 
- We will ignore atmospheric considerations. Compared with the extra 
energy needed to overcome air friction, it would be a relatively trivial
 step to completely burn away the Earth's atmosphere before beginning 
the process. Even with this done, however, this method would require a -
 let me emphasize this - titanic quantity of energy to carry 
out. Building a Dyson sphere ain't gonna cut it here. (Note: Actually, 
it would. But if you have the technology to build a Dyson sphere, why 
are you reading this?) 
 
 
5. Smacking it with something big and hard...
- You will need: a big heavy rock, something with a bit of a swing to it... perhaps Mars.
 
- Method: Essentially, anything can be destroyed if you hit it 
hard enough. ANYTHING. The concept is simple: find a really, really big 
asteroid or planet, accelerate it up to some dazzling speed, and smash 
it into Earth, preferably head-on but whatever you can manage. The 
result: an absolutely spectacular collision, resulting hopefully in 
Earth (and, most likely, our "cue ball" too) being pulverized out of 
existence - smashed into any number of large pieces which if the 
collision is hard enough should have enough energy to overcome their 
mutual gravity and drift away forever, never to coagulate back into a 
planet again.
 
- A brief analysis of the size of the object required can be found here.
 Falling at the minimal impact velocity of 11 kilometres per second and 
assuming zero energy loss to heat and other energy forms, the cue ball 
would have to have roughly 60% of the mass of the Earth. Mars, the next 
planet out, "weighs" in at about 11% of Earth's mass, while Venus, the 
next planet in and also the nearest to Earth, has about 81%. Assuming 
that we would fire our cue ball into Earth at much greater than 11km/s 
(I'm thinking more like 50km/s), either of these would make great 
possibilities.
 
- Obviously a smaller rock would do the job, you just need to fire it 
faster. Taking mass dilation into account, a 5,000,000,000,000-tonne 
asteroid at 90% of light speed would do just as well. For smaller chunks, there are more options - a
 Bussard Ramjet (scoop up interstellar hydrogen at the front and fire it
 out the back as propellant) is one of the most technically feasible as 
of right now. Of course, a run-up would be needed...
 
 
6. Using von Neumann machines
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| Robot sex | 
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- You will need: a single von Neumann machine. 
 
- 
Method: A von Neumann machine is any device that is 
capable of creating an exact copy of itself given nothing but the 
necessary raw materials. Create one of these that subsists almost 
entirely on iron, magnesium, aluminum and silicon, the major elements 
found in Earth's mantle and core. It doesn't matter how big it is as 
long as it can reproduce itself exactly in any period of time. Release 
it into the ground under the Earth's crust and allow it to fend for 
itself. Watch and wait as it creates a second von Neumann machine, then 
they create two more, then they create four more. As the population of 
machines doubles repeatedly, the planet Earth will, terrifyingly soon, 
be entirely eaten up and turned into a swarm of potentially sextillions 
of machines. Technically your objective would now be complete — no more 
Earth — but if you want to be thorough then you can command your VNMs to
 hurl themselves, along with any remaining trace elements, into the sun.
 This hurling would have to be achieved using rocket propulsion of some 
sort, so be sure to include this in your design. 
 
- 
So crazy it might just work.
 
 
7. Total existence failure
- You will need: to wait
 
- 
Method: No method. Simply sit back and twiddle your 
thumbs as, completely by chance, all 
200,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 
atoms making up the planet Earth suddenly, simultaneously and 
spontaneously cease to exist. Note: The odds against this actually ever 
occurring are considerably greater than a googolplex to one. Failing 
this, some kind of arcane (read: scientifically laughable) 
probability-manipulation device may be employed. 
 
- 
Utter, utter rubbish. 
 
- Boring.  
 
If your best efforts fail, you needn't fret. Nothing lasts forever; the Earth is, ultimately, doomed, whatever you do. 
 
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