Originally Posted by Almighty Colin

Rocket science. It's first year physics. You can estimate the velocity needed to escape the Earth by setting the kinetic energy equal to the potential energy and solve for v.

GMm/r = mv^2/2
v = SQRT(2GM/r)

v is about 25,000 miles per hour at the earth's surface. For a rocket you should factor in air resistance too.

So if the earth explodes with enough force to send pieces at the surface out at greater than about 25,000 miles per hour they are not coming back. As the pieces get further apart they will slow down because of the earths gravity but
at the magic 25,000 mph they will always have just enough velocity to always be just a little further out and keep going. The force between any two objects in the Universe falls off as the square of the distance. So when two pieces of Earth move 10 times further apart the gravitational attraction between them is 100 times weaker. When they get 100 times further apart the gravitational attraction becomes 10,000 times weaker.

Oh,yeah. There are other objects in the Universe. You send a chunk of Earth into orbit and it ends up close to Jupiter it might get caught in orbit around Jupiter or crash into it depending on the distance and velocity.