Einstein and GPS. Why our browser would be useless without relativity

Einstein and GPS.  Why our browser would be useless without relativity

GPS (Global Positioning System) was a navigation system created for military applications. It was in the 1980s when it was opened to civil applications. Today it is a free system that consists of at least 24 satellites that make two complete revolutions around the Earth in 24 hours, in 6 different orbital planes, at an altitude of 20,200 km and with a speed of 14,000 km/h. .

The other part of the GPS system is the user’s receiver. Initially they were specific GPS receivers from various brands. Today it can be a watch or a mobile phone with a built-in GPS receiver. For GPS to work, the receiver must be connected to at least three satellites. If it is only connected to three it gives us information about a 2D position. It means in two dimensions, that is, longitude and latitude. If the receiver is connected to four or more satellites, it gives the 3D position (longitude, latitude and height) as well as speed, heading, distance…

With this data, for example, we can move through the mountains without getting lost, or find a street or a house in a city. These applications make GPS very popular among hikers, hunters, mountain bikers, sport fishermen, etc. In addition, they are used in a large number of professional applications. In addition to the military, they are used by fishing and transport boats, by commercial aviation, in automobiles, in surveying work, among the scientific community, etc. Accuracy depends on the price of the receiver. With professionals, who cost thousands of euros, the precision in the position can reach one centimeter. Precision that increases in some military and scientific applications. The first satellite was launched in 1978 and in 1994 the network of 24 was completed. Each satellite is scheduled to be replaced after 10 years.

The accuracy of GPS needs to use the theory of relativity (restricted and special) formulated by Einstein in 1905 and 1916. Let’s look at this need. Each satellite constantly emits a radio signal that is received by our receiver. It provides information on the position of the satellite at the moment in which it emits the signal and the time in which it was emitted (time). For this, the 24 satellites have an atomic clock.

With the data received and the time measured with the receiver’s clock, it calculates its position. In these measurements lies the problem of precision. The theory of relativity shows that time on the satellite, which moves at 4 km/s, passes at a different speed than on Earth. Furthermore, since the gravitational potential (force of gravity) decreases with height, its value on the satellite is lower than its value on the Earth’s surface. According to the theory of relativity, these two effects cause time on the satellite to pass at a different speed than time on Earth.

Although this difference is imperceptible to us, we are talking about 39 millionths of a second per day, if we take into account that the speed of light is very great (300,000 km/s), a simple calculation indicates that the error after one day, If the so-called relativistic correction is not applied, it would be 11.7 km. in the horizontal plane and 700 m. in height. If instead of a day we took a week, the error in height would be 5 km. Can you imagine an urgent rescue of a mountaineer with these accumulated errors? The relativistic correction is called “the factory frequency setting.” It is an adjustment that is made to the atomic clocks of satellites before launching them into space.

As we see, GPS would be of almost no use without taking into account the theory of relativity. In this case, it is not the mechanics of the clock that fails, but rather the physical nature of the universe that causes clocks to measure different times when they travel at different speeds or are in gravitational fields of different intensity.

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