# Albert Einstein and the GPS

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I'm a big fan of Albert Einstein. Many physicists would agree that his theories are the purest expression of genius in the history of humanity with all the ensuing applications. In this case, we talk about the Global Positioning System (GPS).

The GPS was developed by the US military in the middle of the Cold War in the 60s. It was originally used by the navy for navigational purposes. In a previous version, a ship could update the data on the position only once per hour. Over the following decades, the United States has continued to improve the system by launching more satellites. In the 80s, the Reagan administration decided to make available GPS technology for civilian purposes. The impetus for the solution was the Korean Airlines passenger plane shot down by the USSR in 1983, accidentally flying over the Soviet Union on its way from Alaska to Korea.

The GPS system consists of 24 satellites flying around the earth in high orbit. These satellites travel at a speed of about 14.500 km per hour and their orbit is at an altitude of 19.000 kilometres. (For comparison, The orbital altitude of the International Space Station is about 400 kilometres). Each satellite has an atomic clock, the precision of which is about 1 nanosecondo. The satellites are distributed in such a way that from any part of the Earth's surface, at least four of them are in line of sight. A GPS receiver on the ground (or on an airplane in flight) It receives data about the time and location of these satellites using a radiofrequency signal 1,575 GHz.

Without the theory of relativity, Albert Einstein would not exist GPS. Ideas like crazy slow times at higher speed or bend a subject called four-dimensional space-time continuum by a massive object are crucial to the operation of the GPS. Instead of accurately measuring standing (and for the military, in inches) without taking into account of the theories of Einstein, You would be measured just in miles. But for an accurate indication of the path that is not enough. Within a very short period of time, such errors would accumulate and the entire system would become useless.

The GPS receiver can calculate the distance to each satellite from the time taken by the radio waves that propagate at the speed of light. Knowing the exact distance of three satellites encoded within the signal and their position, the microprocessor of the receiver can determine its coordinates by means of trilateration. The trilateration is a more complex form of triangulation, which uses intersecting spheres to determine the location based on the distance from the other three points of the three-dimensional space. a fourth satellite is needed to verify backup and temporary fixes to a non-atomic receiver.

Measure the travel time of radio waves which propagate on these relatively short distances requires an extremely high precision. The GPS requires accuracy to within a few nanoseconds. And this requires an appeal to the special and general theory of relativity of Einstein. Special relativity regards objects moving at high speed, while the general relativity is a theory of gravity.

Einstein published his theory of special relativity in 1905 and forever changed our fundamental ideas about the universe. It showed that in contrast to Newton and common sense, the speed of light, and not the time or the distance, It is a truly universal constant. His theory states that while the speed of an object approaches the speed of light, time slows down in relation to the observer “immobile” on earth. I highlighted the word “immobile” in quotes, because in reality there is nothing Property, and right now we are moving on Earth, making revolutions around the sun in a galaxy which rotates in an expanding Universe

According to the theory of special relativity, if your twin brother fly away on a spaceship at a speed close to the speed of light, his time would slow down in relation to your. It may come back after an hour it was only an hour for him and see that you 50 years his. The time difference depends entirely on how close it is its speed at the speed of light. This effect is known as time dilation and is expressed by the following formula of Lorentz transformation:

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**t** is the time in an inertial reference system (in a system that moves at a constant speed, such as a GPS receiver on Earth),

**t ‘** It is the time in another inertial reference system (for example, a satellite in orbit),

**v** It is the relative velocity between two reference systems,

**c** It is the speed of light.

When the relative velocity is small compared to the speed of light, the above formula is reduced to t '= t, namely the absence of time dilation. This is our everyday world. But when its velocity approaches the speed of light, infinity (that is, time slows down or even stops at the speed of light). For GPS satellites that move at a speed of 14.500 km all'ora, time flows around 7000 nanoseconds per day slower than the receiver's time on Earth.

The reason why the theory of special relativity was defined special is that this theory has had a limit, running only in a special case when the acceleration is zero. The equations of Einstein's special theory of relativity are valid only when the object moves at a constant speed in a straight line in such a way that there is no acceleration.

Einstein, at the end, He realized that the acceleration and gravity are equivalent (the so-called principle of equivalence). In 1915, after almost ten years of struggle with math behind his new theory, He published his masterpiece, general Relativity. The mathematical basis of the general theory of relativity, known as tensor analysis, is many times more complicated than is necessary for the special theory of relativity. After more than 200 years of domination, Newton's theory of gravity was overthrown by Einstein's new theory of gravity.

The general theory of relativity has shown that mass gravity distorts the fabric of space-time continuum. The gravity, as well as the speed in the special theory of relativity, It is because of time dilation. In the case of GPS, satellites in space undergo a slightly lower gravity than a receiver on Earth. Because of this difference of gravity, the time for flowing a satellite 45.000 nanoseconds per day faster than a terrestrial receiver.

The theory of special relativity says that for fast-moving satellites, time slows down, while the general theory of relativity predicts that for satellites, time runs faster because they experience less gravity. The combination of these effects leads to the fact that for the satellites relative to the terrestrial receiver, time passes faster 38.000 (45.000 – 7.000) nanoseconds per day. Radio waves from satellites travel at a speed of about 30 cm per nanosecondo. This means that without relativistic effects, the distance of each satellite will be distorted by about 11,5 Km per day!

Regardless of whether the system shows a direction toward a restaurant, allow pilots to pinpoint their location anywhere in the world or help you find a pet misplaced, GPS affects many aspects of life of each of us. Just remember that if a hundred years ago did not exist a person who passionately wanted to know the nature, everything would be impossible. *"I have no special talents. I'm just curious insanely* “, Albert Einstein once said.

With this I tried to make understandable a topic that has always been his aura of mystery. I certainly do not explain everything in the individual aspects, who is really involved will go into that, for others will say that they know something about it, They have never had the desire to deepen. 😉

Finally! Gorgeous article! Simple concise clear finally written by someone who shows they understand. Congratulations Amilcare

I already knew the fragments of these theories, but this is the first time I managed to merge them all together.

It is also the first time that I was able to follow any explanation to the end.

This article is very well written, thank you!