Where is Earth?

Well I don't think it is unreasonable to assume that earth is one of the central worlds of trader space. I think it's not owned as such by any part of the TEC, as the frontier worlds are, but is rather property of all of humanity.

Being in the very center, it wouldn't be in major danger of Vasari or Advent attack....yet. The Vasari will be content if they can begin their next phase of the Exodus. The Advent, however, would love to wipe out Earth.

The story is ambiguous as to Earth's involvement in the TEC Empire.  It's one of those things that you can choose to interpret as you like.

My personal interpretation on the matter is that Earth's age of dominance has come and gone.  The colonies established by Earth have matured, and many of their people have moved on to colonize new systems.  These people were born outside of the Sol System and to them there is nothing special about it, and they have no particular sense of loyalty to Earth.  As more and more mature colonies develop, Earth would become less and less significant. 

I always just considered it one of the inner core worlds. So at the moment the war is raging on the outer to middle colonies so you won't see it. Too tell you the truth at first I was disappointed that Earth wasn't a planet. I wanted to nuke, glass, and kinetic bolt it!

Another possible theory is that Earth has been destroyed or run out of resources to be of use. Sins doesn't have a starting date, but you know it has been a long time because the Trade Order had been around for 1,000 years and then changed to TEC when the Vasari attacked (as mentioned in the manual). And at that time humans were already settling other worlds. We also don't know when humans invented or discovered the technology to travel to other solar systems. It is a possibility that in that time Earth could have been hit by a large asteroid or all the resources were used up and instead of shipping supplies from other worlds to Earth, people just left.

You could come up with many different theories for this.  

perfect answer really it depends upon your imagination.. when i think of Huma"n(s) i think about a planet called earth

"thats a thing that bothered me about Starcraft... atleast until Broodwar was released.. it all became clear"

I don't really care to know. I've played lots of games, watched TV, and watched many movies. Much of the selection that are space based seem have Earth as some place important merely because its... well... Earth. Having Earth be saved... again, or be some place important for the n-th time will not do it for me.

I'll be quite happy if the devs said that humanity has simply forgot where their place of origin was...

 There are scifi out here (think star wars) where there is no earth.  The back story is such a small part of the game I never gave any thought to as whever there was an earth in this game or not.