GPS is
really an intereting technology
It use a
system of 24 satellites continuously orbiting the earth, and reqires at least four satellites to track your location. It
uses at atomic clock, and the error of your mobile phone is also a matter of
great concern.
Moreover,
albert of relativity play an important role in GPS technology finally a
real-life application for the theory of relativity let’s put aside all these
complications, and understand the technology of GPS is a stap-by-stap and
logical manner.
Let’s assume
that your friend want to find out your location and you have a mobile phone
which has an integrated GPS receiver in GPS, AN INTERESTING mathematical
technique called trilateration is used to locate someone’s position let’s first
understand trilateration in two-dimensional way.
At least two
satellites are required to find out your position in two-dimensional trilateratrion
using some engineering techniques the
satellites measure the distance between you and the satellites
We will see
the techniques for this later. Now thing are easy The first satellite knows you
are at a distance of R1 so, you should be somewhere on this circle . the second
satellite knows you are at a distance of R2 so you should be on this circle as
well
This means
your actual location in short should be on the intersection points, Now there
is a small issue there are two intersection points so , which is you final
position?
For this you
take the Earth’s surface as the third circle. And eliminate the impobable
solution In the three-dimensional world, you can also use the same approach
here instead of two satellites we need three satellites in the
three-dimensional world the satellite knows you are somewhere on a sphere with
the use of a second satellite your position narrows down to a circle
Note that
the intersection of two spheres gives a circle, now with the help of a third
satellite you will be able to narrow down your location to just points here,
the intersections of a circle and a sphere gives two points just like in the
previous case using the earth as the forth surface we find the correct point
the three special coordinates
How lets see how the distance between you and the satellite is measuredAll the satellite are equipped with a very accurate atomic clockThe satellite sends an intermittent radio signal down to earthThis radio signal will contain the exact time the signal was sent, and the position of the satellite assume the receiver also has a very accurate clock.
The receiver
on earth receives the signal Atypical smartphone GPS receiver is shown here
since radio waves travel at the speed of light your receiver receives the
signal after a certain time duration by finding out difference between the send
and received times and multiplying it by the speed of light you will be able to
find out the distance between you and the satellite since the satellite has
already send you its coordinate you can easily build a sphere around the
satellite’s center point and find out your position as explained before one
thing to note here is that the time measurement has to be very accurate even an
error of microseconds will give an error in the tange of kilometers since the
speed of light is so huge here comrs the main issue your receiver accurate
clock.
Your mobile phones or laptop work on crystal clocks that are not accurate when compared to atomic clocks When compared to atomic clocks Having an atomic clocks in a smartphone is simply impractical you can easily see how inaccurate your smartphone clock is compared to an atomic clocks by checking the time settings. We call the diffrernce between to actual time and thr time measured by your mobile phone, as time offset this time offset will cause a huge error in GPS calculations
How do we
overcome this issue?
The good
news is that the time offset of your smartphone with all three of the
satellites is samesince the satellite all keep the same time.
The time
offset value of your device become the new unknown this means apart from the
three special coordinates we have to solve the time offset value of your
receiver as will we need an extra satellite measurement to solve this fourth
unknown and that is why need four satellites to measure your location
This way we
avoid the need of an atomic clock in your mobile device if you check your
current GPS constellation it will be clear that at least four satellite con see
your location at any points in time please hold on, this video is not yet over,
We have one
more issue to solve even with all these advanced technologies this GPS system
will not give you the right location here cones the importance of Einstein’s
theory of relativity time is not absolute it depends upon many other factors
According to
the theory of special relativity a fast moving clock will slow down the atomic
clocks which are moving at speed of 14,000 kilometer per hour, will slow down
by seven microseconds every day, due to this at an altitude of 20,000 kilometer
above earth
The
satellite experience one quarter of the earth’s gravity thus, according to
einstein’s general relativity theory, the clocks will tick Sliqhtly faster in
this case, around 45 microseconds every day
This means a
net 38 microseconds offset is created every day in the atomic clock to
compensate for this a theory of relativity equation is inteqrated into the
computer chips and adjusts the rates of the atomic clocks without this
application of the theory of relativity
The GPS
would have produced an error of 10 kilometer every day GPS is navigation system
developed by the US Department of defense and is completely free for the public
however there are accurate alternatives available in many countries nowadays
modern receivers simultaneously make use of GPS and other navigation system to
get the most accurate position
Now , a
quick question does GPG require an internet connection? GPS does not require an internet, or cell
phone signal however with their help
GPS staeup
can be greatly speeded up satellite location information can be downloaded by
the internet rather than direct satellite downloads which are very slow such
GPS system are known as assisted GPS so the next time you track your food
delivery or navigate your car plsase keep in mind how important the theory of
relativity developed by Einstein and the other mathematical ideas are, behind
GPS
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