Would my helicopter land in a different place?

This is something i have asked myself for years now?
Suppose i have a helicopter and i would take off and go straight up in a vertical line.
Then i would go as high as needed (how high would that be?) as to no longer be bothered by gravity.
I would hover in that position for, let’s say, twelve hours and then i would go back in a vertical line to groundlevel again.
Would i land in a different place/country/continent?
Or are there physics laws that would stop me from this whole experiment in the first place?
Any clever minds here that can shine a light on this?