| Top 10 Ways to Destroy Earth   #3 
Pulverized by impact with blunt instrument
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 kilometers 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. A 10,000,000,000,000-tonne asteroid at 90% of light
speed would do just as well. See the Guide to moving Earth for useful
information on maneuvering big hunks of rock across interplanetary
distances.
Pretty plausible.
Earth's final resting place: a variety of roughly Moon-sized chunks of rock, scattered haphazardly across the greater Solar System.
Earliest feasible completion date: AD 2500, maybe?
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