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« on: January 08, 2015, 02:23:50 PM »
GPS (Global Position System) or more accurately GNSS (Global Navigation Satellite System) proves with absolute certainty that the earth is a spheroid and that our current understanding of geodesy is correct. This fact can be personally verified by anyone that cares to test the validity of GNSS for a few hundred dollars and a few hours of experimentation.
A GNSS receiver can be purchased for about $200 that will output the users position as well as the raw data used to compute that position. It is common knowledge that such systems exist and function accurately as witnessed by anyone who has purchased a high end motor vehicle within the last decade. FET believers explain this with the notion that GNSS is really just a ground based system and that the government or other conspirators have hidden this fact in complex designs of the GNSS chipsets to make the units appear to be using satellites for navigation. Thus the suppose that the position results reported are based on some terrestrial navigation system. However, it is also possible to capture the actual raw data from the receiver, and for the US GPS system (NavStar) these measurements include the Keplerian orbital elements (ephemeris) for each satellite (SV) along with a measurement of the distance between the user and all SVs that are currently being tracked. The SV ephemeris is used to compute the position of each satellite tracked at the time of measurement, then the users position is computed from solving a simple set of equations that relate the users position to the position of each tracked SV (observation equation):
range_to_sv = sqrt((Xuser-Xsv)^2+(Yuser-Ysv)^2+(Zuser-Zsv)^2)+CLKuser*Cvac
Where:
range_to_sv this it the range measurement reported by the receiver
X,Y,Z sv The position of the satellite in ECEF (Earth Centered Earth Fixed)
X,Y,Z user The unknown position of the user
CLKuser The unknown error in the GNSS receiver time.
Cvac Speed of light in a vacuum
Since inexpensive GNSS receivers use simple quartz clocks, the internal time is not very accurate which is the reason the term CLKuser has to be included in the observation equation. Since GNSS uses the time it takes for signals to travel from the satellite to the receiver to compute the distance, the range_to_sv value measured by the receiver will include this clock error. So for the GNSS user, there are four unknowns, the X,Y,Z position of the user, and the error in the GNSS receiver clock. If four or more satellites are tracked, then it is possible to solve the set of equations for the unknown values. Note that the GNSS user not only computes it's position, but also an extremely accurate estimate of the current time. In fact, some GNSS users are only interested in the time solution for the synchronization of clocks.
If a user collects this raw data along with the position results reported by the receiver they will see that all range measurements and SV ephemeris data are consistent with the user position. FET believers may at this point try to explain this by saying that the SV ephemeris and range data is faked by the receiver to make things work. The problem with this argument is that the user can only receive signals from satellites that are in clear view. If there is any obstruction, such as a hill or a tall building, it is not possible to track a satellite blocked by that obstruction. How would it be possible for a faked GNSS system to know when to discontinue providing data for a satellite due to obstructions? It would require a real time 3d model of every hill, tree, building, bridge, tunnel etc. in order to create this faked data. Also, the GNSS system is a receive only system, the transponders are only broadcasting information and only the users GNSS system actually knows where it is, so this real time model would have to be inside the GNSS system. There simply is no possible way to fake the GNSS raw measurements, and the raw measurements show that the GNSS SVs are in an orbit around the earth.
Done, RET proved, solved period.