J
Jeanh
Guest
GPS functions by working out your position from at least 4 overhead satellites.
Although it sounds simple, the entire process is complicated. Let me try my best to explain.
Imagine a modified game of Marco Polo
Instead of me the player trying to figure out where the other players are hiding, imagine that I am blindfolded and trying to find where I am located.
Two further modifications does exist in this game.
Now let me replace my players with satellites in outer space.
24 satellites flying around the Earth together make our GPS system. These satellites are located 20,000 km above us and are moving at a speed of approximately 14,000 km/hr. These will lead to complications about the concept of time but I will get that to later.
Now when the players of my modified Marco Polo game has been replaced by satellites, these new players also let me (GPS receiver) know how far away I am from them and their exact locations.
Also the GPS receiver does not really say "Marco" in real life, it listens to the GPS satellites broadcasting rather passively.
Speed of Light and Other Things Or How To Locate A GPS Receiver
All GPS satellites are broadcasting a pseudo random string of 0s and 1s which is known only to the receiver. By figuring the delay between broadcasted and the received signal, the distance from the satellite can be calculated by multiplying it by the speed of light. Now this is usually done for 4 satellites and the position of the GPS receiver can be figured out in 3 dimensions (latitude, longitude,altitude).
Sounds Simple. Wait Time Is Relative !
GPS systems are meant to be accurate within 5 to 8 meters. If you consider the speed of light (300,000,000 m/s) that means that translates to a time accuracy of something like 20 to 30 ns. A nanosecond is a billionth of a second and this matters when it comes to GPS.
GPS satellites contain super accurate clocks onboard called Atomic Clocks which use decay time of energy levels of individual atoms to be accurate within 1 ns. So everything seems good then.
Einstein's Relativity. Time Is Not Same Anywhere.
Remember Interstellar, where the astronauts being close to massive black hole slowed time so much that a minute there translated to several years on Earth. Einstein's relativity shows up when it comes to GPS and without correcting for it we would never be able to accuracy we have today.
Special Relativity
Special Relativity tells us that 'the faster we go, time slows down."
The satellites are in orbital velocities of 14,000 km/hr. Although this is nowhere near the speed of light this makes the clock on the satellite tick 7 microsecond slower than a clock on earth per day.
General Relativity
Put simply, General Relativity states that 'closer you are to a massive object, time slows down'.
The GPS receiver is much closer to a massive object, Earth than the satellite. Now this makes the Earth Clock tick 45 microsecond slower per day than the space clock.
Now putting it all together, the total delay is 45-7=38 microsec.
The Space Clock is always 38 microsec ahead of the Earth clock per day.
In conclusion, if these effects are not taken into account, GPS would stop being accurate after 2 minutes of use. A receiver gets all these information from all the 4 satellites and works out the delays, relative times and velocities to give the final location.
Although it sounds simple, the entire process is complicated. Let me try my best to explain.
Imagine a modified game of Marco Polo
Instead of me the player trying to figure out where the other players are hiding, imagine that I am blindfolded and trying to find where I am located.
Two further modifications does exist in this game.
- Not only the other players shout out polo, but they somehow manage to convey how far away they are from me.
- The players know their own individual locations very well and they convey that information to me as well.
Now let me replace my players with satellites in outer space.
24 satellites flying around the Earth together make our GPS system. These satellites are located 20,000 km above us and are moving at a speed of approximately 14,000 km/hr. These will lead to complications about the concept of time but I will get that to later.
Now when the players of my modified Marco Polo game has been replaced by satellites, these new players also let me (GPS receiver) know how far away I am from them and their exact locations.
Also the GPS receiver does not really say "Marco" in real life, it listens to the GPS satellites broadcasting rather passively.
Speed of Light and Other Things Or How To Locate A GPS Receiver
All GPS satellites are broadcasting a pseudo random string of 0s and 1s which is known only to the receiver. By figuring the delay between broadcasted and the received signal, the distance from the satellite can be calculated by multiplying it by the speed of light. Now this is usually done for 4 satellites and the position of the GPS receiver can be figured out in 3 dimensions (latitude, longitude,altitude).
Sounds Simple. Wait Time Is Relative !
GPS systems are meant to be accurate within 5 to 8 meters. If you consider the speed of light (300,000,000 m/s) that means that translates to a time accuracy of something like 20 to 30 ns. A nanosecond is a billionth of a second and this matters when it comes to GPS.
GPS satellites contain super accurate clocks onboard called Atomic Clocks which use decay time of energy levels of individual atoms to be accurate within 1 ns. So everything seems good then.
Einstein's Relativity. Time Is Not Same Anywhere.
Remember Interstellar, where the astronauts being close to massive black hole slowed time so much that a minute there translated to several years on Earth. Einstein's relativity shows up when it comes to GPS and without correcting for it we would never be able to accuracy we have today.
Special Relativity
Special Relativity tells us that 'the faster we go, time slows down."
The satellites are in orbital velocities of 14,000 km/hr. Although this is nowhere near the speed of light this makes the clock on the satellite tick 7 microsecond slower than a clock on earth per day.
General Relativity
Put simply, General Relativity states that 'closer you are to a massive object, time slows down'.
The GPS receiver is much closer to a massive object, Earth than the satellite. Now this makes the Earth Clock tick 45 microsecond slower per day than the space clock.
Now putting it all together, the total delay is 45-7=38 microsec.
The Space Clock is always 38 microsec ahead of the Earth clock per day.
In conclusion, if these effects are not taken into account, GPS would stop being accurate after 2 minutes of use. A receiver gets all these information from all the 4 satellites and works out the delays, relative times and velocities to give the final location.