Feasibility rating: 5/10

**Blown up by matter/antimatter reaction**You will need: 2,500,000,000,000 tons of antimatter

Antimatter - the most explosive substance possible - can be manufactured in small quantities using any large particle accelerator, but this will take some considerable time to produce the required amounts. If you can create the appropriate machinery, it may be possible - and much easier - simply to "flip" 2.5 trillion tons of matter through a fourth dimension, turning it all to antimatter at once.

Method: This method involves detonating a bomb so big that it blasts the Earth to pieces.

How hard is that?

The gravitational binding energy of a planet of mass M and radius R is - if you do the lengthy calculations - given by the formula E=(3/5)GM^2/R. For Earth, that works out to roughly 224,000,000,000,000,000,000,000,000,000,000 Joules. The Sun takes nearly a WEEK to output that much energy. Think about THAT.

To liberate that much energy requires the complete annihilation of around 2,500,000,000,000 tonnes of antimatter. That's assuming zero energy loss to heat and radiation, which is unlikely to be the case in reality: You'll probably need to up the dose by at least a factor of ten. 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=mc^2) should be sufficient to split the Earth into a thousand pieces.

Earth's final resting place: A second asteroid belt around the Sun.

Earliest feasible completion date: AD 2500. Of course, if it does prove possible to manufacture antimatter in the sufficiently large quantities you require - which is not necessarily the case - then smaller antimatter bombs will be around long before then.