How Theory of Relativity act on our day-to-day life?

We are all familiar with the Special and General relativity theory, Some novices may feel that the theories are for highly knowledgeable people but the reality is not like that. The mathematical proof of the theory may be tough for laymen but the truth is that these theories have deep root application in our daily life. Everyone can understand its application without any hassle.

The application for special and general relativity theory came in the global positioning system (GPS). Now the GPS technology is a part of our day-to-day life. Before knowing in detail about the application of the theory in daily life we need some knowledge about the working principle of the global positioning system.

Global Positioning System consists of a cluster of 24 satellite orbiting earth. The GPS technology we are enjoying on our mobile phones and other navigation devices is the result of the combined function of these 24 satellites.

These 24 satellites are orbiting the earth in six orbits. That means four satellites in each orbit. Because of this special kind of orientation of satellite each and every corner of the earth came under the service limit of the global positioning system.

All of these satellites are orbiting at a height of 20,000 km. each satellite took twelve hours to complete one rotation. Atomic clocks are installed in these GPS satellites, they are synchronized with clocks on earth. Only three GPS satellites are needed to detect the position of a GPS receiver on earth. with the help of a fourth GPS satellite, the GPS system will find out the altitude of the receiver.

These satellites frequently send data to receivers on the ground to calculate time and distance. For example consider three satellites named Satellite 1, Satellite 2, and Satellite 3.

If one of these satellites sends a signal to a receiver on the ground the GPS device will calculate the distance using the distance formula. 

Distance = Speed X Time

Here the signals are traveling at the speed of light so we can consider the speed as C= 3X10^8 m/s.

FIG 1

The circle shown around satellite 1 is the probable area at which the GPS receiver on earth lies, these figures are in two-dimension consider it as a three-dimensional sphere. After this, satellite 2 will also do the same process.

FIG 2

So there will be an overlapped area between the range of these two satellites. SO the GPS system can assume that the GPS receiver on earth lies somewhere on the overlapped area. The third satellite (Satellite 3 ) also do the same process to calculate the distance between the GPS receiver on earth and satellite 3. The intersecting point of these three circles in FIG 3 will exact the position of the GPS receiver on earth.

FIG 3

The position of the GPS receiver will be on the point intersecting these three circles. You may be thinking that how Albert Einstein's relativity theory is related to the global positioning system.

As per the Special theory of relativity time dilation will happen to an object moves faster. This means time on a fast-moving object like a satellite will be lesser than a slow-moving object or stationary object like the GPS receiver on earth. 

The GPS satellites are moving at a speed of 39 km/s. The fast-moving satellite will be slowed by 7  microseconds in a day relative to the GPS receiver on earth. This is a fact as per the special relativity theory. 

As per the General theory of relativity, clocks run slower when gravity is more. So the clocks on earth get 45 microseconds slower per day than clocks on satellite.

Dilation due to the Special Theory of relativity is -7 microsecond
Dilation due to the General Theory of relativity is 45 microseconds

There will be an error of 38 microseconds (45 microseconds - 7 microseconds = 38 microseconds) in calculating the time in distance formula (Distance = Speed X Time). 

This means that the clock on the satellite is running 38 microseconds faster than the clocks on earth. This error of 38 microseconds will decrease the accuracy of the Global Positioning System by 10 km per day.

Don't worry about the accuracy of your GPS navigation system. It is showing accurate location because Scientists and engineers programmed these satellites to overcome this error. 

This is how the theory of relativity plays its role in our day-to-day life.