27/03/2019

Without Einstein's 'useless' discoveries, GPS wouldn't exist.

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

The Global Positioning System (GPS) was created by the United States Department of Defense for military purposes and later opened for civilian use. Currently, other countries have similar systems.

The advent of mobile devices has made GPS accessible to everyone, making it one of the technological advancements with the most evident impact on our lives.

What is less known is that the system could not function without Albert Einstein's most famous discovery, the theory of relativity, begun in the "miracle year" of 1905 and completed in 1915.

To explain this, we need to understand how GPS works. I thank reader Alison Moraes, senior technologist at the Institute of Aeronautics and Space, for his detailed explanations.

The core equipment of GPS is a constellation of satellites orbiting the Earth, which emit electromagnetic signals that identify the satellite and provide the exact time of emission.

The signals are received by our devices (cell phones, for example), which know the exact time of reception. Therefore, since the electromagnetic signal travels at the speed of light, we can calculate the distances of the device in relation to each of the satellites.

From there, since the positions of the satellites are also known, to obtain the position of the device it is only necessary to solve a fairly simple system of equations.

In theory, it would be enough to have the distances to four satellites, but in practice it is necessary to use more to increase reliability. And, to ensure that a sufficient number of satellites are accessible at all times from any point on the Earth's surface, the constellation needs to be relatively large: currently there are 31 satellites.

The system error is currently between 5 and 10 meters, and with the ongoing improvements, it should drop to a few centimeters.

This is an incredible feat because, even though the explanation above may seem simple, in practice there are many difficulties. Among others, the clocks on the satellites need to be perfectly synchronized with those on the ground—the allowed margin of error is only 20 nanoseconds (0.000000020 seconds). And that's where the theory of relativity becomes indispensable.

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