Re: to sam

Tom Potter wrote:


Here we are, 100 years after General Relativity
and it continues to generate more hype and heat
than light and advances.


Real-World Relativity: The GPS Navigation System
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

People often ask me "What good is Relativity?" It is a commonplace
to think of Relativity as an abstract and highly arcane
mathematical theory that has no consequences for everyday life.
This is in fact far from the truth.

Consider for a moment that when you are riding in a commercial
airliner, the pilot and crew are navigating to your destination
with the aid of the Global Positioning System (GPS). Further, many
luxury cars now come with built-in navigation systems that include
GPS receivers with digital maps, and you can purchase hand-held GPS
navigation units that will give you your position on the Earth
(latitude, longitude, and altitude) to an accuracy of 5 to 10
meters that weigh only a few ounces and cost around $100.

GPS was developed by the United States Department of Defense to
provide a satellite-based navigation system for the U.S. military.
It was later put under joint DoD and Department of Transportation
control to provide for both military and civilian navigation uses.

The current GPS configuration consists of a network of 24
satellites in high orbits around the Earth. Each satellite in the
GPS constellation orbits at an altitude of about 20,000 km from the
ground, and has an orbital speed of about 14,000 km/hour (the
orbital period is roughly 12 hours - contrary to popular belief,
GPS satellites are not in geosynchronous or geostationary orbits).
The satellite orbits are distributed so that at least 4 satellites
are always visible from any point on the Earth at any given instant
(with up to 12 visible at one time). Each satellite carries with it
an atomic clock that "ticks" with an accuracy of 1 nanosecond (1
billionth of a second). A GPS receiver in an airplane determines
its current position and heading by comparing the time signals it
receives from a number of the GPS satellites (usually 6 to 12) and
triangulating on the known positions of each satellite. The
precision is phenomenal: even a simple hand-held GPS receiver can
determine your absolute position on the surface of the Earth to
within 5 to 10 meters in only a few seconds (with differential
techiques that compare two nearby receivers, precisions of order
centimeters or millimeters in relative position are often obtained
in under an hour or so). A GPS receiver in a car can give accurate
readings of position, speed, and heading in real-time!

To achieve this level of precision, the clock ticks from the GPS
satellites must be known to an accuracy of 20-30 nanoseconds.
However, because the satellites are constantly moving relative to
observers on the Earth, effects predicted by the Special and
General theories of Relativity must be taken into account to
achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion
relative to them, Special Relativity predicts that we should see
their clocks ticking more slowly (see the Special Relativity
lecture). Special Relativity predicts that the on-board atomic
clocks on the satellites should fall behind clocks on the ground by
about 7 microseconds per day because of the slower ticking rate due
to the time dilation effect of their relative motion.

Further, the satellites are in orbits high above the Earth, where
the curvature of spacetime due to the Earth's mass is less than it
is at the Earth's surface. A prediction of General Relativity is
that clocks closer to a massive object will seem to tick more
slowly than those located further away (see the Black Holes
lecture). As such, when viewed from the surface of the Earth, the
clocks on the satellites appear to be ticking faster than identical
clocks on the ground. A calculation using General Relativity
predicts that the clocks in each GPS satellite should get ahead of
ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the
clocks on-board each satellite should tick faster than identical
clocks on the ground by about 38 microseconds per day (45-7=38)!
This sounds small, but the high-precision required of the GPS
system requires nanosecond accuracy, and 38 microseconds is 38,000
nanoseconds. If these effects were not properly taken into account,
a navigational fix based on the GPS constellation would be false
after only 2 minutes, and errors in global positions would continue
to accumulate at a rate of about 10 kilometers each day! The whole
system would be utterly worthless for navigation in a very short
time. This kind of accumulated error is akin to measuring my
location while standing on my front porch in Columbus, Ohio one
day, and then making the same measurement a week later and having
my GPS receiver tell me that my porch and I are currently about
5000 meters in the air somewhere over Detroit.

The engineers who designed the GPS system included these
relativistic effects when they designed and deployed the system.
For example, to counteract the General Relativistic effect once on
orbit, they slowed down the ticking frequency of the atomic clocks
before they were launched so that once they were in their proper
orbit stations their clocks would appear to tick at the correct
rate as compared to the reference atomic clocks at the GPS ground
stations. Further, each GPS receiver has built into it a
microcomputer that (among other things) performs the necessary
relativistic calculations when determining the user's location.

Relativity is not just some abstract mathematical theory:
understanding it is absolutely essential for our global navigation
system to work properly!
.

Relevant Pages

  • Re: Myth of GPS Employing the Nonsense of SR and GR
    ... I wouldn't have thought GR was relevant to GPS? ... People often ask me "What good is Relativity?" ... GPS satellites are not in geosynchronous or geostationary orbits). ... their clocks ticking more slowly (see the Special Relativity ...
    (sci.physics.relativity)
  • Re: Simple experiments that conclusively disprove General Relativity
    ... continually controls the oscillators and clocks on the GPS satellites. ...
    (sci.physics)
  • Re: to sam
    ... Real-World Relativity: The GPS Navigation System ... GPS satellites are not in geosynchronous or geostationary orbits). ... their clocks ticking more slowly (see the Special Relativity ...
    (sci.physics)
  • Re: to sam
    ... Einstein's Relativity and Everyday Life ... But GPS is an exception. ... twice per day, much faster than clocks on the surface of the Earth, ... The net result is that time on a GPS satellite clock advances ...
    (sci.physics)
  • Real-World Relativity: The GPS Navigation System
    ... Real-World Relativity: The GPS Navigation System ... GPS satellites are not in geosynchronous or geostationary orbits). ... their clocks ticking more slowly (see the Special Relativity ...
    (sci.geo.satellite-nav)
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