How GPS works.
The GPS system consists of 24 satellites orbiting 12,000 miles above
the earth. The satellites are tracked by radar and frequently updated
with their exact positions relative to the earth.
Each satellite also has an atomic clock that is accurate to within a few
one-billionths of a second (nanoseconds) per day. Every satellite knows
precisely where it is and precisely what time it is. The satellites
broadcast this information to your GPS receiver.
Your GPS receiver has a clock that is synchronized with the atomic
clocks on the satellites. With these synchronized clocks it can measure
the time it takes for the signal to travel from a satellite to the
receiver. Knowing that the radio signal travels at 299,792,458 meters
per second, your receiver can now calculate its exact distance from the
With the signal from one satellite, the receiver now knows that it is
somewhere on an imaginary bubble with the satellite in the middle. Where
that bubble intersects the earth, it forms a circle. The GPS receiver knows
it is somewhere on that circle.
|With the signal from one satellite your GPS receiver knows you are somewhere on a circle on the earth's surface.
With the signal from another satellite the receiver knows it is
also somewhere on another circle. Therefore, it knows that it is at one
of the two places where these two circles intersect.
|With the signal from two satellites, your GPS receiver knows you are at one of two places where two circles intersect.
With the signals from a third satellite the receiver knows it is
somewhere on yet another circle. The receiver then knows that it is at
the one point where all three circles intersect.
|With the signal from three satellites, your GPS receiver knows you are at the one place where all three circles intersect.
That is how the GPS pinpoints your position on the earth.
Except this can’t work. The satellites have atomic clocks that are accurate
to a few nanoseconds per day. The receiver has a quartz clock that is
accurate to perhaps half a second per day. The receiver needs to synchronize
its clock with the atomic clocks on the satellites. It can only do this if
it knows precisely how far it is from each satellite. However, the receiver
can’t know how far it is from the satellites unless its clock is
synchronized with the clocks on the satellites.
The receiver solves this problem with a simple trick. It calculates its
location, not caring if the clocks are perfectly synchronized. If its clock
is off, there will be no one place where all three circles line up.
the receiver clock is not synchronized with the satellite clocks, there
will be no one place where all three circles intersect.
The receiver adjusts its clock until all three circles cross at one point.
|The receiver adjusts its clock until all three circles intersect in one place.
Now the receiver's quartz clock is synchronized with the satellite's atomic
clocks, and the receiver knows exactly where it is.
This would work perfectly if the earth were a uniform sphere, but it’s
not. The earth is an oblate spheroid, flattened at the poles and
bulging at the equator.
|The earth is not a sphere. It is an oblate spheroid.
It’s also covered with continents and mountains. The receiver needs a
signal from a fourth satellite to get its location in three dimensions.
That position is superimposed on a map of the earth, and we’re done.
Except for altitude? The receiver knows exactly where it is, but we
want to know how high we are above sea level, but is sea level? Once
again, the earth is not a sphere. Also, some parts of the earth
have stronger gravity than others. Water is pulled to these areas of high
gravity, making sea level higher at these places than elsewhere. For
example, the beaches
around India are much closer to the center of the earth than the
beaches around Ecuador. A GPS receiver has a map of mean sea levels
around the world. It adjusts the altitude according to its location on the earth. Now we have a
working GPS system that tells you exactly where you are and how high
you are above sea level.
This would be it, except for a little problem called special relativity. The
GPS satellites are 12,000 miles from earth. At this distance, gravity is a
bit weaker than on the earth’s surface. Thanks to special relativity, time
passes faster where gravity is weaker. The atomic clocks on the GPS
satellites run 52 one-millionths of a second (52 microseconds) faster per
day than atomic clocks on the earth. On the other hand, the satellites are
moving at thousands of miles per hour relative to the earth. This makes the
clocks on the satellites run seven microseconds per day slower than they
would on the earth. The net result is that the atomic clocks on the GPS
satellites gain 45 microseconds per day relative to atomic clocks on the
earth. This will cause your GPS receiver to drift by 10 kilometers per day.
At least that's what you may have heard, but that's a myth. As long as the
clock in the receiver is synchronized with the clocks in the satellites, you
will get an accurate position. There is no need to synchronize the atomic
clocks on the satellites with atomic clocks on the earth. However, with such
accurate clocks on the GPS satellites, why not compensate for special
relativity and get the correct time as well as our position on the earth? To
this end, the atomic clocks in the GPS satellites are designed to lose 45
microseconds per day to compensate for special relativity. They are also
updated once per week to keep them synchronized with earth-based atomic
clocks, just so they can tell us what time it is.
And that’s how GPS works.