Pertinent question regarding time traveling

[Calabi_Yau]

Suppose I traveled back in time 10 seconds. As the Earth is revolving around the sun at a great speed, I would end up in outer space as the Earth 10 seconds ago hasn't yet reached my actual position.

Or, as time and space are connected, would I still end up where I am sitting now, but 10 seconds in the past, and perhaps on the lap of my past self? And more, if space has many dimensions, is it possible that time also has more than one dimension? Could we somehow be affected by higher time dimensions?

 

[mfb]

There are no universal (time-independent) positions in space, but any time-travelling device would have to take locations into account to be useful.