Silverana-I noticed there was an oversight in answering your question "i just gotta get this piece of information confirmed ... is the geodesic for earth our equator? " The principle of extremal aging (from General Relativity) summarizes the result that a free particle follows a geodesic, a worldline of extemal aging. Principle of extremal aging: The path that a free particle takes between two events in spacetime is the path for which the time lapse between these events, recorded on its wristwatch, is an extremum. This path is a path in which the free particle follows its natural motion (free fall, no force acting upon the free particle to change its path) in the gravitational field (curved spacetime). It is the straight line through curved spacetime. Deimos mentioned the Riemann geometry which is the geometry Einstein used for his theory of gravity, General Relativity.