- [Narrator] GPS has already become
an integral part of our lives,
And you can see a few useful applications
from these examples.
(upbeat music)
GPS is really an interesting technology.
It uses a system of 24 satellites
continuously orbiting the Earth,
and requires at least four satellites
to track your location.
It uses at atomic clock,
and the time error of your mobile phone
is also a matter of great concern.
Moreover, Albert Einstein's theory of relativity
plays 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 step-by-step and logical manner.
Let's assume that your friend
wants 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 a two-dimensional way.
At least two satellites are required
to find out your position in two-dimensional trilateration.
Using some engineering techniques,
the satellites measure the distance
between you and the satellites.
We will see the techniques for doing this later.
Now things 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
should satisfy both these circles.
In short, you should be on the intersection points.
Now there is a small issue.
There are two intersection points.
So, which is your final position?
For this you take the Earth's surface as the third circle,
and eliminate the improbable 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 two points.
Here, the intersection 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 spacial coordinates.
Now, let's see how the distance between you
and the satellite is measured.
All the satellites are equipped
with a very accurate atomic clock.
The satellite sends an intermittent
radio signal down to Earth.
This 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.
A typical 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 the difference
between the sent and received times,
and multiplying it by the speed of light,
you will be able to find out
the distance between you and the satellites.
Since the satellite has already sent 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 range of kilometers,
since the speed of light is so huge.
Here comes the main issue.
Your receiver does not have a highly accurate clock.
Your mobile phones or laptops,
work on crystal clocks that are not accurate
when compared to atomic clocks.
Having an atomic clock in a smartphone,
is simply impractical.
You can easily see how inaccurate
your smartphone clock is compared to an atomic clock,
by checking the time settings.
We call the difference between to actual time,
and the 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 the same,
since the satellites all keep the same time.
The time offset value of your device
becomes the new unknown.
This means, apart from the three spacial coordinates,
we have to solve the time offset value
of your receiver as well.
We need an extra satellite measurement
to solve this fourth unknown,
and that is why we 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 satellites
can see your location at any point 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 comes 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 kilometers per hour,
will slow down by seven microseconds every day, due to this.
At an altitude of 20,000 kilometers above the Earth,
the satellites experience one quarter
of the Earth's gravity,
thus, according to Einstein's general relativity theory,
the clocks will tick slightly 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 integrated
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 kilometers 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 systems,
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 startup 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 systems are known as assisted GPS.
So, the next time you track your food delivery,
or navigate your car,
please keep in mind how important the theory of relativity,
developed by Einstein,
and the other mathematical ideas are, behind GPS.
Thank you for watching the video,
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