PROFESSOR: Welcome back to A20 special relativity.
In this last section of this chapter,
we talked about applications and implications
of special relativity.
We talked about the global positioning system.
You all have used GPS before, be it in your car
when you're trying to find your way through town
or when you go for a run and you want to measure how long
and how fast you actually are running.
The global positioning system is a set
of satellites all equipped with atomic clocks.
And they're used for navigation and have been developed first
under the name of Napster GPS.
And GPS is one of many global or few global navigation system.
Others are GLONASS, BDS, Galileo Systems developed in Europe,
in Russia, in Japan, and so.
This picture here shows you how you
want to view this view of Earth and then at around 20,000
kilometer, GPS has about 31 satellites,
which zooms around the Earth.
And as soon as you have three satellites, which
you can see from your viewpoint, you
can actually figure out where that viewpoint is.
Think about each satellite gives you an information of a sphere.
The cross section between two spheres is a line.
And if you have three spheres crossing,
that gives you three-dimensional information about location
on which you're looking at this.
GPS was-- the first satellites were launched in 1978.
Again, 31 satellites in orbit at the time right now.
So how does this work?
So the satellite transmits information
about position in time in regular intervals.
It's does have a clock.
They use a specific frequency or multiple frequency
to send signals.
And then the receiver calculates how far away the satellite is
and how long it took the message to arrive
at the place of the receiver.
Again, three satellites are used to extract the exact location.
However, as you can imagine, the reason
why I bring this up in this class
is that we have to consider effects
of special relativity and also, general relativity,
as we will discuss later in this class.
So you have clocks on the satellites.
And you have identical clocks on Earth.
And they do tick differently as we discussed many times
in this class.
If you were to calculate the effect of special relativity,
the prediction is that the clocks
take about 7 microseconds a day slower on the satellite
then compared to the one on Earth.
However, the satellite at a higher orbit.
And the gravitational pull at a higher orbit
is less strong as on Earth.
And that then, as a result, is the clocks
on the satellites actually run faster than the ones on Earth.
And that effect is larger, very larger
than the effect of special relativity, which
is effect from then just moving relative to the observer.
The fact is 47 microseconds a day.
And then you can just calculate the net correction,
which is 38 microseconds a day, which corresponds
to about 11 kilometers.
Now imagine on your run and there's
11 kilometer difference a day.
I don't expect you to run for a day,
but you might run for an hour.
Still the effect is rather large.
So you want to have a more precise system.
And therefore, those effects need to be corrected,
and they are.
They're typically built in into the electronics
and automatically corrected.
The precision achieved with GPS system
ranges a little bit based on how you use the information, what
kind of transceiver you use.
It's in the order of 505 meters to 30 centimeters,
so about this of a distance.
So anywhere on this planet you can pinpoint your location
by about this with this precision.
Well, this concludes the discussion
of implications and applications in special relativity.