With classical physics it is also possible the correction of the clocks on the GPS.

The correction of the clocks on the GPS is announced as one of the biggest hits of the theory of general relativity, but this work exposes that the clocks in the satellite systems, not only can be corrected with Albert Einstein's theory of relativity, but also with the theory of classical physics. Based on a mathematical formula that has been published by Paul Gerber in 1898, as the solution to explain the anomaly of the perihelion of mercury, it also makes a relationship in the theoretical explanation of classical physics, and the techniques of parabolic flight, as the experimental way to confirm the theory of Gerber. Finally concludes that the correction of the clocks on the GPS has two theoretical ways to express themselves, but a single mathematical form.

Introduction;  

We have all heard that without the theory of relativity the GPS fail in its navigation function.

Einstein's theory of general relativity says that the curves of gravity space and time, giving rise to a tendency for the clocks in orbit around dial a little faster, the clocks on the satellites are moved to 14,000 km/hr in orbits that revolve around the Earth twice a day, much faster than the clocks on the Earth's surface. The net result is that the time in a clock of GPS satellite moves faster than a clock on the ground by about 38 microseconds per day.

The response of relativity to this time-lag is originated from the mathematical formula which Albert Einstein in 1915 responded to the anomaly on the advance of the perihelion of mercury, based on their conception of curvature of space and time.

Paul Gerber (born in 1854 Berlin, Germany, and died August 13 1909 Freiburg, Germany) was a German physicist known for his controversial work in the speed of gravity and the change of perihelion of the orbit of Mercury.

The mathematical formula with which he explained the anomaly of the perihelion of mercury was;

This formula is mathematically identical to that of Albert Einstein (1915) from general relativity. But his theory is very different, while Albert Einstein stated in his theory that the anomaly of the perihelion of mercury is caused by the curvature of space time, Paul Gerber (1898) he said, that the force between two masses could be corrected by a term that depends on the speed at which these masses are moved.

The atomic clock is a type of clock to feed its counter uses a frequency of atomic resonance normal. The best references atomic frequency (or clocks) modern are based on physical more advanced involving cold atoms and atomic.

The atomic clocks maintained a timeline continuous and stable, the Atomic time (TAI). For everyday use is spreading another time scale: the Coordinated Universal Time (UTC). The UTC is derived from TAI, but synchronized using seconds of collation with the Universal Time (UT1), which is based on transition day-night according to the astronomical observations.

Physicists at the National Institute of standards and technology (NIST), USA, where the first atomic clock in 1949, have achieved a double record of accuracy with a clock pilot that uses atoms of strontium instead of cesium. His calculations suggest that the agents that affect the ticking atomic, such as gravity or electromagnetic fields, it would need 15,000 million years to make the clock will delay or advance a second.

Parabolic Flight is a flying technique in which an aircraft ready for it (the cab of the passage is empty and cushions, at least in part) drops in a controlled manner to that in its interior get a state similar to that of the free fall in a vacuum. This maneuver allows it to simulate the effect of microgravity for short periods of time in the inside of the appliance.

By the time it reaches the 6000 meters of altitude, approximately, the plane maintains (or starts, if this is the case) a climb at an angle of 47 º, which causes a sensation of on gravity in its interior of between 1.8 and 2 g. By reaching out to about 8000 m changes the trajectory, begins a tilt lower progressive during which the power of the engines low up to a minimum which is used to counteract the resistance of the air, The sensation of gravity low to values close to zero. After a few seconds of lowering aircraft will progressively increased, with what the sensation of gravity increases gradually, the engines are increasing power to level the appliance on the 6000 m and ascends again, returning to suffer a effect on gravity, and this way alternatively.

Results;

The GPS could also be corrected by the mathematics of classical physics, and more precisely because the mathematical formula of the German physicist Paul Gerber, is equal to the one described by Albert Einstein to give answers to the malfunction of the perihelion of mercury, formula that is used for the correction on the clocks on the GPS. The differences between the two answers to the malfunction of the perihelion of mercury are only theoretical. While Einstein was recognized by explain this anomaly as the result of the curvature of space time, Paul Gerber makes it from the perspective of classical physics as the result the force of the masses as consequences of the difference in the speeds.

But in recent years, the theory of Gerber seems to be strengthened, not only because he was the first to explain mathematically the anomaly of the perihelion of mercury, but now a flying technique called parabolic flight, confirm all the days, experimentally that Gerber also had the theoretical reason.

We know that the atomic clocks can be affected by the force of gravity, and this force also depends on the speed, as we see experimentally in the technique of parabolic flight, now the gravity produced by the curvature of space time as theorized Albert Einstein, is more complicated to verify experimentally.

Conclusion;

It can be concluded that the clocks in satellite systems, not only can be corrected with the theory of general relativity, but also with the theory of classical physics on gravity, based on the mathematical formula that published Paul Gerber in 1898, which GPS not would fail in his navigation function, if it disappeared relativity. In addition the theoretical explanation of Paul Gerber may be proven experimentally by parabolic flight techniques. Finally it can also say that the correction of the GPS has two theoretical ways to express themselves, but a single mathematical form. 

Bibliography;

http://physicscentral.com/explore/writers/will.cfm.

https://en.wikipedia.org/wiki/Paul_Gerber

https://es.wikipedia.org/wiki/Reloj_at%C3%B3mico

http://elpais.com/elpais/2015/04/21/ciencia/1429625205_847314.html

https://es.wikipedia.org/wiki/Vuelo_parab%C3%B3lico

https://es.wikipedia.org/wiki/Gravedad

http://www.cienciapopular.com/experimentos/gravedad-cero

http://francis.naukas.com/2010/08/02/la-historia-de-la-anomalia-en-el-avance-del-perihelio-de-mercurio-y-la-formula-de-gerber-einstein/