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Einstein and GPS. Our browser would not work without relativity

The GPS (Global Positioning System/Global Positioning System) is a navigation system that was originally developed for military purposes.

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Einstein and GPS. Our browser would not work without relativity

The GPS (Global Positioning System/Global Positioning System) is a navigation system that was originally developed for military purposes. In the 1980s, civilian applications were allowed to use it. It is now a free system with at least 24 satellites. They circle the earth twice per hour in six orbital planes at an altitude 20200 km and a speed of 14,000 km/h. .

The receiver is the other component of the GPS system. They were originally designed to be specific receivers for different brands of GPS. It can be a watch, a phone or a mobile device with a GPS receiver. GPS receivers must be connected at least to three satellites in order to function. It will only give us information about a 2D location if it is connected to just three satellites. It refers to two dimensions: longitude and latitude. The receiver can be connected to more than four satellites and it will give the 3D position (longitude latitude, height, speed, heading, distance).

This data allows us to navigate through mountains without getting lost or locate a street or house in a town. These apps make GPS extremely popular with hikers, hunters and mountain bikers . They are also used in many professional applications. They are also used in military operations, fishing, transport, and commercial aviation. The price of the receiver will determine the accuracy. The precision of the position can be as high as a centimeter with professional receivers, which can cost thousands of euro. Some military and scientific applications have a higher accuracy. In 1978, the first satellite was launched. The 24-member network was complete in 1994. Every satellite will be replaced after 10 years.

The theory of relativity, which Einstein developed in 1905 and 1916, is necessary to ensure GPS accuracy. Let's look at this need. Every satellite emits a radio frequency signal which is picked up by the receiver. It provides information about the satellite's position at the time it emits the radio signal (the time) and its time. The 24 satellites are equipped with an atomic clock.

The receiver calculates its position using the data received and time measured with the receiver clock. The problem with accuracy lies in these measurements. The theory of relativity states that the time on the satellite moves at 4 km/s and passes at a different speed from Earth. The satellite's gravitational potential (force gravity) is also lower than that on the Earth because it decreases with height. These two effects, according to the theory relativity, cause time on satellite to move at a different speed from time on Earth.

This difference may not be obvious to us but it is still significant. If we consider that light travels at a very fast speed (300,000 km/s), we can calculate that the error after one-day, if relativistic correction isn't applied, would be 11.7 km. in the horizontal plane, and 700 m. in elevation. The error in height would be 5km if we took a week instead of one day. These accumulated errors can be used to rescue mountaineers. "The factory frequency setting" is a relativistic correction. This is an adjustment made to satellite's atomic clocks before they launch them into space.

Without the theory of relativity, GPS would not be useful for nearly anything. It is not the mechanical failure of the clock, but the physical nature and strength of the universe that causes clocks to measure time differently when traveling at different speeds or in gravitational fields with different strengths.

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