Advanced Space Travel

In thinking about the heat that we have in the center of the Earth, it seems as though we have a huge supply of energy that isn't going away any time soon.  The gravity from the Earth causes all the matter in the world to compress towards the center creating large amounts of heat. 

Eventually this is going to be useful as we figure out how to use it.  One way that may be especially interesting is for space travel.  I know, there's no way to take the energy with you.  But really, what we could do is actually make the entire Earth a space ship and use the energy that it creates by it's own gravity to drive the ship.  Some day this may become a reality, and while taking Earth to distant galaxies may not work out or be advisable, it might be a good idea for a nearby planet.