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.
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.
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).
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.
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