GPS, How does it work

GPS has already become an interal of part of our lives And you can see a few useful applications for these examples.

GPS is really an intereting technology

It use a system of 24 satellites continuously orbiting the earth, and reqires at least  four satellites to track your location. It uses at atomic clock, and the error of your mobile phone is also a matter of great concern.

Moreover, albert of relativity play an important role in GPS technology finally a real-life application for the theory of relativity let’s put aside all these complications, and understand the technology of GPS is a stap-by-stap and logical manner.

Let’s assume that your friend want to find out your location and you have a mobile phone which has an integrated GPS receiver in GPS, AN INTERESTING mathematical technique called trilateration is used to locate someone’s position let’s first understand trilateration in two-dimensional way.

At least two satellites are required to find out your position in two-dimensional trilateratrion  using some engineering techniques the satellites measure the distance between you and the satellites

We will see the techniques for this later. Now thing are easy The first satellite knows you are at a distance of R1 so, you should be somewhere on this circle . the second satellite knows you are at a distance of R2 so you should be on this circle as well 

This means your actual location in short should be on the intersection points, Now there is a small issue there are two intersection points so , which is you final position?

For this you take the Earth’s surface as the third circle. And eliminate the impobable solution In the three-dimensional world, you can also use the same approach here instead of two satellites we need three satellites in the three-dimensional world the satellite knows you are somewhere on a sphere with the use of a second satellite your position narrows down to a circle

Note that the intersection of two spheres gives a circle, now with the help of a third satellite you will be able to narrow down your location to just points here, the intersections of a circle and a sphere gives two points just like in the previous case using the earth as the forth surface we find the correct point the three special coordinates

How lets see how the distance between you and the satellite is measuredAll the satellite are equipped with a very accurate atomic clockThe satellite sends an intermittent radio signal down to earthThis radio signal will contain the exact time the signal was sent, and the position of the satellite assume the receiver also has a very accurate clock.

The receiver on earth receives the signal Atypical smartphone GPS receiver is shown here since radio waves travel at the speed of light your receiver receives the signal after a certain time duration by finding out difference between the send and received times and multiplying it by the speed of light you will be able to find out the distance between you and the satellite since the satellite has already send you its coordinate you can easily build a sphere around the satellite’s center point and find out your position as explained before one thing to note here is that the time measurement has to be very accurate even an error of microseconds will give an error in the tange of kilometers since the speed of light is so huge here comrs the main issue your receiver accurate clock.

Your mobile phones or laptop work on crystal clocks that are not accurate when compared to atomic clocks When compared to atomic clocks Having an atomic clocks in a smartphone is simply impractical you can easily see how inaccurate your smartphone clock is compared to an atomic clocks by checking the time settings. We call the diffrernce between to actual time and thr time measured by your mobile phone, as time offset this time offset will cause a huge error in GPS calculations

How do we overcome this issue?

The good news is that the time offset of your smartphone with all three of the satellites is samesince the satellite all keep the same time.

The time offset value of your device become the new unknown this means apart from the three special coordinates we have to solve the time offset value of your receiver as will we need an extra satellite measurement to solve this fourth unknown and that is why need four satellites to measure your location

This way we avoid the need of an atomic clock in your mobile device if you check your current GPS constellation it will be clear that at least four satellite con see your location at any points in time please hold on, this video is not yet over,

We have one more issue to solve even with all these advanced technologies this GPS system will not give you the right location here cones the importance of Einstein’s theory of relativity time is not absolute it depends upon many other factors

According to the theory of special relativity a fast moving clock will slow down the atomic clocks which are moving at speed of 14,000 kilometer per hour, will slow down by seven microseconds every day, due to this at an altitude of 20,000 kilometer above earth

The satellite experience one quarter of the earth’s gravity thus, according to einstein’s general relativity theory, the clocks will tick Sliqhtly faster in this case, around 45 microseconds every day

This means a net 38 microseconds offset is created every day in the atomic clock to compensate for this a theory of relativity equation is inteqrated into the computer chips and adjusts the rates of the atomic clocks without this application of the theory of relativity

The GPS would have produced an error of 10 kilometer every day GPS is navigation system developed by the US Department of defense and is completely free for the public however there are accurate alternatives available in many countries nowadays modern receivers simultaneously make use of GPS and other navigation system to get the most accurate position

Now , a quick question does GPG require an internet connection?  GPS does not require an internet, or cell phone signal however with their help

GPS staeup can be greatly speeded up satellite location information can be downloaded by the internet rather than direct satellite downloads which are very slow such GPS system are known as assisted GPS so the next time you track your food delivery or navigate your car plsase keep in mind how important the theory of relativity developed by Einstein and the other mathematical ideas are, behind GPS