If someone were to transmit short wave "Skywave" from the equator in the UTC+0 timezone (Greenwich Time) with vertical polarization, and the receiver is at the equator ~10000km away in the UTC-6 timezone (Galapagos Time), given enough transmission power, what would be the polarization of the received signal?
Assuming that the magnetic and gravitational field strength are consistent in all locations along the path of travel and that the reflections off of the surface of the earth do not affect the polarization. Also assuming that the transmitter and receiver are both at sea level, and that the reflections off of earths surface are all at sea level on a perfectly smooth surface. The time is also midnight half-way between the receiver and transmitter, so "Skywave" conditions are optimal.
EDIT: Knowing that the ionospheric radio reflection may or may not randomize the polarization of a reflection, lets simply assume all reflections act as if they are reflecting off of an idealized radio reflector.