Assuming that a method was found to teleport objects, and at huge range, if an object was teleported from the surface to a location at the correct height (wikipedia says about 42,164 km from earth's center of gravity if I'm reading it correctly) and directly above it's point of origin and maintained all momentum, would it arrive in a geosynchronous orbit? The momentum transfered from it's surface velocity should be exactly the velocity of an object in geosynchronous orbit if my understanding of orbital mechanics is correct, and thus it should be in geosynchronous orbit.
Teleporting the object to a location closer to earth should result in it being at the apoapsis of an elliptical orbit and on it's way back down towards earth, and if it was teleported low enough it would eventually collide. Teleporting an object further would result in it being at the periapsis of an elliptical orbit and if teleported far enough it would actually leave earth's orbit.
The question comes as a result of me thinking over design concepts for a physics-heavy game involving space travel and ultimately future technology and trying to wrap my head around how all of these various types of science-fiction technology would actually interact with orbital mechanics.