moving the gaze Google-earth rotating and let the target point move to center
Cool! I’m not sure how rotating would work. Assuming you’ve stopped rotating though, moving the viewport and screen to make the point of gaze more near the center sounds useful and natural.
It would be just like the eye-tracking demos that have a window automatically scroll down when your gaze reaches the bottom of the window. In the case of Google maps, or Google Earth, all the edges come into play, and different parts of the edges would have different degrees of movement.
A faster navigation option might be to latch onto the nearest notable location or landmark, and make that the center.
(I just opened Google Earth on my tablet, and you see a whole bunch of bus stops scattered around. There probably needs to be a two-step process (magnification, or projection of the bus-stop elements into larger interface elements: http://i.imgur.com/3erfG6K.png) to pick the exact one that you want to center on).
For rotating, maybe you can activate a widget that ceases movement by way of changing your location. The edges then instead become controls that manipulate the pitch and yaw.
As for navigating in Google Street view, check out “Controlling a PlayStation with your eyes: ‘Infamous: Second Son’ | GDC 2014” at the 33 second mark: http://youtu.be/kKYr9MaZw3I?t=33s
Anyways, good luck!