How does GPS work? Fascinating.

How does your Mobile phone know exactly where you are ?

Published in

Shyam Cortex

4 min readMar 29, 2018

**“A satellite in orbit over the cloudy skies” by** **NASA** on **Unsplash**

The answer lies 12,000 miles above your head, in an orbiting satellite that keeps time to the beat of the atomic clock powered by quantum mechanics.

Lets break that down. First of all, why is it important to know what time is it in the satellite when location is what we are concerned about.

The first thing your phone needs to determine is how far is it from a satellite.
Each satellite constantly broadcasts radio signals that travels from space to your phone at the speed of light. Your phone records the signal arrival time to calculate the distance to the satellite using the simple formula distance equal c times time(distance = c * t), where c is the speed of light and t is the distance traveled by the signal .

But there’s a problem, light is incredibly fast so every location on earth would seem to be the same distance from the satellite.

To keep up this time we use Atomic clock which are so accurate they would gain or lose a second even if they ran for the next 300 million years. Atomic clocks are made in such a way so that they read time so accurate within 1 billionth of a second.

Einstein’s theory of relativity kicks in with the atomic clocks.

GPS satellites have atomic clocks on board to keep accurate time. General and Special Relativity however predict that differences will appear between these clocks and an identical clock on Earth.

Special Relativity tells us that moving clocks run slower with respect to a stationary observer. This slowing of time becomes more obvious as something approaches the speed of light. Satellites do not travel anywhere near the speed of light, however they are travelling very fast compared to an observer on the ground, so the effect is measurable.
General Relativity says that the closer you are to a heavy mass, such as Earth, the slower time will move for you. This means that a clock on a satellite orbiting the Earth will run faster relative to one on the ground.

The whole GPS network has to make allowances for these effects — proof that Relativity has a real impact.

GPS satellites travel at approximately 14,000 km/h (8,700 mph) with respect to Earth. This means time runs 7.2 microseconds per day slower for a satellite relative to us on Earth as described by Special Relativity.

However, using General Relativity it is possible to calculate that time goes faster for a GPS satellite by 45.9 microseconds per day, due to the satellite being 19,000km above the Earth (therefore in weaker gravity). This means overall time runs 38.7 (45.9–72.0) microseconds faster per day for a GPS satellite relative to us stationary on Earth.

So basically the GPS satellites travel in time.

**Atomic clock.(AA size battery for scale)**

We use the concept of Trilateration.

So lets assume that you are fixed in the same place for this moment. So we know that you are at the fixed location from the satellite A, in other words you are somewhere on the sphere centered around the satellite. Measure your distance from the satellite B and you get a overlapping, keep doing this and with just 4 satellites you can pinpoint your exact location.