How GPS works?

Global Positioning System

       The cost for launching some 12 to 24 satellites into the space from our atmosphere with those big satellite launching vehicles needs a huge amount of money, hundreds of scientists for tremendous amount of calculations, good engineering in the sense mechanical, electrical, computational, etc. and finally some hard work.   

      Thinking about all these things, we may think for a while that the GPS system in our mobile does really needs a huge amount of technology. But it is really amazing is that the physics behind this small GPS thing in our smartphones is not more than the level of 10th standard physics. 

       The principle is just,  Velocity [1] =  distance / time . It is all needed to determine the position of an object (ofcourse for the most accurate results we will need some of general and special relativity).

The concept is simple as we determine the distance between two stations in a highway. For example, if you go from station-1 to station-2 with some constant Velocity , the distance between them can be calculated as, $$ Distance(d)_{1-2}= velocity(v) \times time(t)$$
where t - time taken for you to reach from station 1 - 2.

If you don't want to go, you can send a messenger(msg) to station-2 at constant velocity and make him to travel back at the same velocity. Now, you can calculate the time taken for him to travel twice the distance ($d_{1-2}$) with velocity "v". Hence, $$ d_{1-2-1} = 2* d_{1-2} = v_{msg}* t_{msg} $$ or simply $$ d_{1-2} = \frac {v_{msg}*t_{msg}} {2}$$ That is all we need to determine the position of station-2. 

In an exact similar way, satellite determines your position by sending a messenger to your smartphone and receiving it.
And the messenger, in god's grace always travel with same speed in vacuum, Electromagnetic waves. All these things happened just because of EM waves and its constant fundamental speed.

We get all the information so fast because of the tremendous speed of light which is about $3\times 10^8 m/s$
[Think: If it is about some 1 km/s, then before knowing your GPS coordinates, you would have gone to hell.] 

Ok.. Now I can determine the position with light signals. 
But why do you need some 12 to 24 satellites in the space to determine your position?
It is because unfortunately our satellites don't have any eyes. They can just only receive the signals but can never determine accurately "from which direction the signals are coming".

Your position on earth is with respect to the satellite is not a fixed straight line as we did it in the highway problem. 

From the measurements, satellites will determine the position of your cellphone but on the surface of giant hollow sphere centered about the satellite. Since, it knows the signal is coming from earth, it just focuses on the circle that is on earth which is the common intersection hollow sphere about satellite on earth. 




















Thus it reduces the problem of determining the position from infinite space to a small circle on earth. 

We know from geometry that, minimum three circles are needed to intersect to create a point. And so, to determine a position on earth, at least we need three satellites which is visible to that place. You cannot receive and determine the position from the satellite that is on the other side of the earth. 

One or three satellites are not enough to cover the entire globe of sphere. That is why, we are sending so many satellites such that at any point on earth at any time should be covered by at least three satellites in visible range so that all the single points and positions on earth can be located most accurately. 

That is all for the basic lever. 
         But it may not so simple as it sounds, if you are going to need too much accurate and perfect solutions such as determining the distance between your couch and your T.V. from the far distance orbiting satellites. 

        For those things, you will need to finish your degree in Physics, since it handles with synchronization of clocks with the help of special and general relativity.  

[To understand how Relativity plays the crucial role in GPS tracking, we will need some calculations].