Again. Not talking about movement. You're grasping at straws. Please go back and reread the conversation.
It doesn't matter if you wait for the stars to move 6000 miles away from you, or you move to another spot on earth 6000 miles away, forcing those stars towards the horizon, the concept is the same. The stars are not going to build up at the horizon because they are all moving relative to each other when they descend towards the horizon.
Yet they shouldn't descent at all, but that's a whole different topic.
This isn't about movement, it's about seeming location. Your two planes at different altitudes scenario is not the same as what we're talking about. If the stars are 5100km above the surface of the earth, then they are at the same altitude as each other. So let me pitch a scenario to you.
If two planes are flying at 40,000 feet while maintaining 0 relative velocity to each other, which means, for all who don't know, that they are staying the
exact same distance from each other and maintaining the
exact same airspeed, then as they move away, the should appear to approach one another. As things fade into the distance, they appear to get smaller. Since these two objects and traveling exactly equal in relation to one another, we can treat them as the same object. That object should appear to get smaller.
The above scenario should be happening with the stars. Yes, 6000 miles is a huge difference and should appear as such, but it does not. The stars to not appear to move in relation to one another as they should, shown by the scenario I just presented.