[music]
The global positioning system or GPS is
a network of 30 satellites orbiting
about 20,000 kilometres above the Earth.
They send out continuous signals
that tell where that satellite is and at
what time the signal was sent. What the
receiver does - the receiver takes that
signal, decodes it, and calculates how far
away this receiver is from the satellite.
By comparing four different satellite
signals the receiver is able to
determine exactly where it is. So what
we're going to do here is do a quick
little demo of that on a world map.
And because we can't really do the three
dimensional version of it, what we're
going to do is kind of pretend the
world is flat. The
mathematics involves just using
Pythagorean theorem and other than that
it's just working with scales on a map.
So let's say I get a signal - I'm
somewhere in Europe and I get a signal
from a satellite that says I am 20,000
kilometres above Stockholm and
it takes about 68.27 milliseconds for
the signal to travel to you. So where
could you possibly be? Well, by using a
little bit of Pythagorean theorem I can
calculate that - I can figure out okay so
the satellite is 20,000
kilometres above and the signal is going
to travel along the hypotenuse of the
triangle, so I can calculate how far
across on my map I would be. And so when
I do that, I get a value and then
according to my map I have to scale it,
so I start at Stockholm, which is right
here, and
I draw a circle. And my circle goes
out and basically what this says is that
anywhere along that circle I could be.
Now my receiver looks for another
satellite, and with 30 satellites there's
always at least six to eight satellites
visible. So let's listen to another
satellite. And another satellite says - I'm
over Rome - and it takes 67.67
milliseconds to arrive
from Rome. So now I put my pin in Rome
and I draw a circle around Rome. And what
I see is there are two places where the
circles overlap - those are my two
possible locations. So now all I need is a
third satellite, and that third satellite
is going to tell me where I am for sure.
And so the third satellite on my
pretend model here says - I'm over Dublin -
and it takes 67.59 milliseconds
to reach you - so where are you?
And you see that the three circles
overlap above Portugal - in fact above
Lisbon. Now this is just a simple
activity you can do - it's actually a fun
game you can actually have the students
hide themselves and give
clues to each other to say "Can you find
me?" And what happens in real life is you
have to have a fourth signal and that
fourth signal is to verify the time and
the altitude and that puts it into
three dimensions. But other than that
this is a thing called trilateration
and this is how the GPS system
determines where you are.
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