The speed of light is only a local speed limit. Relative speeds of objects distant to each other can exceed the speed of light. This is in response to your statement:

***our relative speed would be greater than the speed of light, ***

The best example is our universe.

Right now our ability to see out into space is limited by the Big Bang. That is the universe is not yet old enough for us to be limited by space expanding away from us at speeds greater than the speed of light.

But in 5 billion years that will be the case. By that time our ability to see the universe will be limited by an event horizon (like in a black hole) where space is receding from us at the speed of light. However, until that time we will see the beginning of the universe (the CMBR) before we get to the point where the universe is going away from us at a relative speed greater than the speed of light. We cannot see past the CMBR because light did not propagate at those early times.

After 100 billion years, if the acceleration of the universal expansion holds, we will be barely able to see beyond our local cluster because the expansion speed is so high (>c). The local cluster might have collapsed by then anyway.

yanniru