We learned that GPS identifies the position of an object using distance measurements from at least three satellites. Let us now examine how distance from the satellites is calculated.
The underlying principle is nothing but the simple rule ‘speed multiplied by travel time gives distance’. For instance, we are told that a train takes three hours to reach from city A to city B at a speed of 80miles per hour. We obtain the distance from city A to city B as 240 miles by multiplying the speed of 80 miles per hour with the travel time of three hours.
In GPS, we are calculating the distance using the time radio signals take to travel from the satellites, so the speed is taken as the velocity of light which is 186,000 miles per second. The variable element here is the time, which can be tricky to measure.
The timing can be tricky due to a number of factors. The times are going to be very short, to the order of a fraction of a second. Therefore we need very precise clocks to measure the timing. However let us assume for the moment that we have very accurate clocks and get on with the process.
For this, both the satellite and the GPS receiver transmit a particular signal called the ‘Pseudo Random Code’ at exactly the same time. Since the signal from the satellite has to travel through space to reach the GPS station, the satellite signal reaches a little later than the signal sent by the receiver.
The two signals would be slightly out of sync this way. If the signals have to coincide, the receiver’s signal timing would have to be adjusted. The amount we have to adjust the receiver’s signal is equal to the time the satellite signal took to travel through space. This time multiplied by the speed of light is the distance from the satellite.
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