| Topic: |
Science > Physics |
| User: |
"Tom Potter" |
| Date: |
19 Dec 2003 07:03:51 AM |
| Object: |
The facts about GPS and GR |
As Mike Varney was kind enough to alert me to a typo,
( I typed "299 792 .458 meters per second"
rather than
"299,792,458 meters per second"),
I am reposting the article
with the typo corrected.
==============
There have been many posts
asserting that General Relativity
is essential to the GPS system.
As the WHO boiler-room seems to be on holiday break,
I have time to explain how satellites are used to
provide precision navigation,
without invoking General Relativity.
1. Light travels at a constant speed
of 299,792,458 meters per second
in the absence of matter,
and in media with sparse matter,
such as the Earth's atmosphere.
2. Time interval measurements of E-M waves in air, and space,
are equivalent to distance measurements.
distance = time interval * C
3. Synchronized clocks can be used to
quantize the distance between the points
by measuring the time it takes light/radio waves
to travel from one point to another.
Clock(A) sends a message that it is time(X).
Clock(B) notes that it is time(X) + I1 on its' clock.
The distance between the clocks is
I1 * C
In other words, systems of synchronized clocks
can quantize the distances between the clocks,
by transmitting the time at each clock's location.
Any clock can determine the distances
between it and other clocks,
by simply determining time(I) for all of the other clocks.
For example,
if one measures a time delay of "I1" of a radio wave
from New York, they must be somewhere on
the surface of a sphere, with a distance radius of I1 * C,
centered about New York
If they also measure a time delay of "I2" of a radio wave
from San Francisco, they must be somewhere on
the surface of a sphere, with a distance radius of I2 * C,
centered about San Francisco.
If they measure both,
they must be on a circle represented by the
intersection of the two spheres.
As can be seen, the measurement of a third point,
would be the intersection of the circle with
another sphere, and would let tell the observer that
they are on one of two points.
A fourth measurement would resolve the situation,
and tell them at which of the two points they are
located.
4. As the GPS satellites are moving,
whereas New York and San Francisco are located
at fixed points (With respect to Earth bound observers.),
it is necessary that GPS receivers know where
the satellites were when they transmitted the time.
This is handled, by having each satellite
transmit its' position in space, along with
the time data.
Each satellite not only transmits where it is ("ephemeris data"),
it transmits its' orbital data ("almanac data"),
along with its' time.
The "ephemeris data"
serves the same purpose to the GPS receiver,
as the Sun does is to a sailor with a sextant.
5. Ground stations continuously monitor
the satellites' orbits and transmissions,
and when changes exceed certain amounts,
signals are sent to the offending satellites,
updating their "almanac data", their "ephemeris data",
their time settings, and drift in their clocks
with respect to the master clock on Earth.
In other words, the ground station monitors the data
transmitted by the satellites and when necessary
sends them signals that tells them, that their
clock is x nano-seconds fast, their orbit has changed to
such and such (Perhaps because of dust drag, etc.),
that their "ephemeris data" should be xxx, etc.
The GPS clocks are set,
to some reference time,
just as your digital watch is,
the only difference being that
the ticks are far more stable, and much finer,
nanoseconds, rather than tenths of seconds.
Drifts in oscillators are corrected by
inserting "ticks", and by adjusting
divider circuits to divide by the desired count.
6. As portable GPS receivers do not have
extremely stable oscillators, they must
derive precision times from the satellites.
As the satellites are at an altitude of about 11,000 miles,
(From the center of the Earth.)
and radio waves travel 186,000 miles in one second,
it takes about .006 seconds for the
time, ephemeris, and almanac data
to reach a sea level receiver.
This means that in a typical transmission,
the GPS receiver must subtract about .006 seconds
from its' clock, in order to set its' clock.
GPS receivers receive and average the times
from several satellites, and recursively
home in on the master time, and make an adjustment
for recursively computed position of the satellite.
In other words, at the reception of the first data,
the GPS receiver knows the master time to about .006 seconds
higher than the first time it receives,
and as it picks up signals from other satellites,
and recursively computes the distances to the
satellites, and averages out multi-path signal variations,
its' own clock homes in on the master clock time.
As the satellites take about 12 hours
(43200 seconds) to orbit the Earth,
and the ephemeris data takes about .006 seconds
to reach the receiver, this means that
the GPS receiver knows where the
satellite is to an accuracy of about one part in
43000 / .006 = 71600000 parts,
even without clock and ephemeris corrections.
Considering that the Earth is about
24,000 miles or 126,000,000 feet in circumference,
this amounts to a sphere of uncertainty of about
1.76 feet at sea level.
7. The clocks used in the GPS system are extremely stable.
They have a long term and short term stability
of about 1 part in 10^14 over one day and even months.
As there are about 3 x 10^13 MICROseconds in a year,
this means that the GPS clocks can maintain microsecond
agreement for over a year, even if no corrections are made.
But of course, adjustments ARE made to the clocks
on a regular basis by a ground clock,
to which all of the GPS clocks are referenced to.
8. As the satellites have a life expectancy of about 10 years,
their orbits are very stable.
In other words, when ground stations get a fix on a satellite's orbit,
we know pretty much where the satellite will be for a long time, and
GPS receivers on the ground have an extremely dependable target to sight on
9. There is some variation in the time it takes the
signal to reach the receiver due to multi paths
taken by the radio wave to the GPS receiver,
so GPS receivers are programmed to compute out the
multi-path variations, and to compute the time,
using the most reliable data it gets from
several satellites.
10. The GPS satellites broadcast on two carrier frequencies:
L1 at 1575.42 MHz and L2 at 1227.6 MHz.
They transmit a "coarse acquisition code" at 1.0 bits per nanosecond and
a "precision code" at a bit rate of 10.230 bits per nanosecond.
As light travels at about 300,000,000 meters per second,
or 300 meters in one micro-second,
a one nano second error would result in an error sphere of about .3 meters
( One foot), and a 10 nanosecond error would
result in an error of about 3 meters or ten feet.
By averaging data from multiple satellites,
a receiver can reduce the timing uncertainty
due to multipaths, and can reduce the error sphere
by only averaging where the error spheres
of several satellites overlap.
The single largest contributor to time transfer uncertainty is path delay,
the delay introduced as the signal travels from the satellite
to the receiver.
In order to measure the time interval most accurately,
a quasi-random code is used. The GPS receiver performs
a auto-correlation on the quasi-random signal
in order to eliminate the jitter in the leading edge
of the transmitted signal, caused by transmitter noise,
receiver noise, environmental noise, multipath signal combining,
jamming, etc.
In other words, a segment of the quasi-random signal is
incrementally delayed, and multiplied by the signal stream.
If two string of random numbers are multiplied,
a maximum occur when and if the strings match,
otherwise the product tends toward zero.
The Military can play games with the GPS signals by
juggling the "precision code" signals,
and thus messing up the accuracy
to which a GPS receiver can the time interval.
In summary, the largest contributor
to time transfer uncertainty is caused by
variations path delay, due to signals reflected
off mountains, buildings, etc., and as note,
much of the path delay errors can be averaged out,
because the satellites are moving, and signals
are received from several satellites.
The best GPS receivers can,
by using the methods addressed above,
reduce the uncertainty in time to about one nanosecond,
which amounts to a sphere of uncertainty of about one foot.
The errors due to GR effects,
aren't even a factor in the GPS system.
It is interesting to see that an oft quoted
( By the GR pushers )Neil Ashby states:
"It is not easy right now to perform relativity tests using GPS
because satellite clocks are actively corrected
to within 1 microsecond of Universal Coordinated Time."
As can be seen, the corrections that are sent to
the GPS clocks to
"actively correct to within 1 microsecond of Universal Coordinated Time."
are a clear indication of how the clocks on the ground,
and the clocks on the satellites differ,
and that an examination of these corrections would
clearly show what differential effects were operative.
The bottom line is,
that the hype that GR was and is essential to the GPS
system, is just that hype, and if there are effects in
space and at orbital velocities that do affect clocks,
the data is available to determine this to parts in 10^14.
I suggest that General Relativity is a Tower of Babel,
used by charlatans to pretend to be privy to esoteric knowledge,
and to con taxpayers out of their hard-earned money,
and that it is not a viable, cost-effective
approach to ANY real world problem.
GR, like Aristotle's physics, Marxism, and Freudism,
has diverted man's time, energy and resources
away from methods that are more viable and cost-effective,
and has sent man off on a detour.
Hopefully, it won't be a 1500 year detour,
as it was in the case of Aristotle.
--
Tom Potter http://tompotter.us
===============
WHO instigates conflict and war for power and wealth?
WHO instigated the class wars of the 1900's?
WHO is instigating the religious wars of the 2000's?
WHO has a well organized propaganda machine?
WHO gang attacks all who expose their agenda and methods?
Visit my web site, and download the world's best physics tutorial!
===============
.
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| User: "Mu-Pi" |
|
| Title: Re: The facts about GPS and GR |
19 Dec 2003 12:32:00 PM |
|
|
"Tom Potter" <tdp@hotsheet.com> wrote in message
news:brusuk$7rii4$1@ID-188019.news.uni-berlin.de...
As Mike Varney was kind enough to alert me to a typo,
( I typed "299 792 .458 meters per second"
rather than
"299,792,458 meters per second"),
I am reposting the article
with the typo corrected.
==============
There have been many posts
asserting that General Relativity
is essential to the GPS system.
As the WHO boiler-room seems to be on holiday break,
I have time to explain how satellites are used to
provide precision navigation,
without invoking General Relativity.
1. Light travels at a constant speed
of 299,792,458 meters per second
in the absence of matter,
and in media with sparse matter,
such as the Earth's atmosphere.
BZZZT! DOA moron. I gave you the correct link... here it is again.
Try once more.
http://www.what-is-the-speed-of-light.com/refractive-index.html
Even with my help your are too retarded to get even the simplest things
correct. How were you ever toilet trained I wonder.
.
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| User: "Dirk Van de moortel" |
|
| Title: Re: The facts about GPS and GR |
19 Dec 2003 07:28:14 AM |
|
|
"Tom Potter" <tdp@hotsheet.com> wrote in message news:brusuk$7rii4$1@ID-188019.news.uni-berlin.de...
As Mike Varney was kind enough to alert me to a typo,
( I typed "299 792 .458 meters per second"
rather than
"299,792,458 meters per second"),
I am reposting the article
with the typo corrected.
==============
There have been many posts
asserting that General Relativity
is essential to the GPS system.
As the WHO boiler-room seems to be on holiday break,
I have time to explain how satellites are used to
provide precision navigation,
without invoking General Relativity.
1. Light travels at a constant speed
of 299,792,458 meters per second
in the absence of matter,
and in media with sparse matter,
such as the Earth's atmosphere.
with a refractive index n = 1.0003 that would
typically be about 299,700,000 m/s.
That is a difference of about 90 km/s.
Ninety kilometers per second.
Dirk Vdm
.
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| User: "Richard Herring" |
|
| Title: Re: The facts about GPS and GR |
19 Dec 2003 07:57:05 AM |
|
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In message <3fe2fd4e$1@usenet01.boi.hp.com>, Dirk Van de moortel
<dirkvandemoortel@ThankS-NO-SperM.hotmail.com> writes
"Tom Potter" <tdp@hotsheet.com> wrote in message
news:brusuk$7rii4$1@ID-188019.news.uni-berlin.de...
As Mike Varney was kind enough to alert me to a typo,
( I typed "299 792 .458 meters per second"
rather than
"299,792,458 meters per second"),
I am reposting the article
with the typo corrected.
==============
There have been many posts
asserting that General Relativity
is essential to the GPS system.
As the WHO boiler-room seems to be on holiday break,
I have time to explain how satellites are used to
provide precision navigation,
without invoking General Relativity.
1. Light travels at a constant speed
of 299,792,458 meters per second
in the absence of matter,
and in media with sparse matter,
such as the Earth's atmosphere.
with a refractive index n = 1.0003 that would
typically be about 299,700,000 m/s.
That is a difference of about 90 km/s.
Ninety kilometers per second.
Worse than that. Within the ionosphere it's less than 1, down to as low
as 0.9999 at GPS frequencies. That's a difference in phase velocity of
tens of km/s in the opposite direction. And the group velocity will be
different again.
--
Richard Herring
.
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| User: "Dirk Van de moortel" |
|
| Title: Re: The facts about GPS and GR |
19 Dec 2003 08:06:35 AM |
|
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"Richard Herring" <junk@[127.0.0.1]> wrote in message news:Lj8SRBSxOw4$EwG2@baesystems.com...
In message <3fe2fd4e$1@usenet01.boi.hp.com>, Dirk Van de moortel
<dirkvandemoortel@ThankS-NO-SperM.hotmail.com> writes
"Tom Potter" <tdp@hotsheet.com> wrote in message
news:brusuk$7rii4$1@ID-188019.news.uni-berlin.de...
As Mike Varney was kind enough to alert me to a typo,
( I typed "299 792 .458 meters per second"
rather than
"299,792,458 meters per second"),
I am reposting the article
with the typo corrected.
==============
There have been many posts
asserting that General Relativity
is essential to the GPS system.
As the WHO boiler-room seems to be on holiday break,
I have time to explain how satellites are used to
provide precision navigation,
without invoking General Relativity.
1. Light travels at a constant speed
of 299,792,458 meters per second
in the absence of matter,
and in media with sparse matter,
such as the Earth's atmosphere.
with a refractive index n = 1.0003 that would
typically be about 299,700,000 m/s.
That is a difference of about 90 km/s.
Ninety kilometers per second.
Worse than that. Within the ionosphere it's less than 1, down to as low
as 0.9999 at GPS frequencies. That's a difference in phase velocity of
tens of km/s in the opposite direction. And the group velocity will be
different again.
Aaarg! Shhhh!
I was saving that for later ;-)))
Dirk Vdm
.
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| User: "Keith Stein" |
|
| Title: Re: The facts about GPS and GR |
21 Dec 2003 04:00:33 AM |
|
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The following simple basic program shows how the time dilations on
satellites are worked out. Even if you are not a computer programmer
you should find you can understand this, that's the nice thing about
BASIC eh!
==================================================
PRINT "This program gives the SR and GR predicted time-dilations for"
PRINT "an Earth Satelite in a circular orbit, at any given altitude."
PRINT
REM VALUES OF THE PHYSICAL CONSTANTS USED
c = 2.99792E+08
G = 6.67259E-11
m = 5.976E+24
R = 6378000
DO: REM prompt user for 'ALTITUDE OF SATALITE'
PRINT
PRINT "Enter M (or m) to simulate the 'MIR Space Station at 300 km'"
PRINT
PRINT "OR Enter G (or g) to simulate the 'GPS Satelites at 20,000 km'"
PRINT
INPUT "OR Enter the altitude of the satelite in 'km' "; h$: PRINT
h = VAL(h$) * 1000
IF h$ = "M" OR h$ = "m" THEN h = 300000!: PRINT "MIR SPACE STATION"
IF h$ = "G" OR h$ = "g" THEN h = 2E+07: PRINT "GPS SATELITES"
LOOP UNTIL h > 0
velocity = SQR(G * m / (R + h))
gamma# = (1 - velocity ^ 2 / c ^ 2) ^ -.5
SRtd = (gamma# - 1) * 24 * 60 * 60
GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60
NETtd = INT((GRtd + SRtd) * 10 ^ 7) / 10
PRINT "Altitude = "; h; "m"
PRINT "Velocity = "; INT(velocity); " m / s "
PRINT "gamma = "; gamma#
PRINT "Time lost per day due to SR time dilation = "; SRtd; "sec"
PRINT "Time lost per day due to GR time dilation = "; GRtd; "sec"
PRINT
PRINT "Net time lost per day in satelite = "; NETtd; "micro sec"
PRINT
PRINT
PRINT
PRINT "N.B. These are Einstein predictions, not mine! - K.Stein "
----------------------------------------------------------------------------
Results from above program:
1. The 'MIR' Space Laboratory(Altitude = 300 km)
Velocity = 7727 m/s SR time dilations = +2.87 E-5 seconds/day
GR time dilations = -2.70 E-6 second/day
Net time dilation = +26 micro seconds/day
and 2. The 'GPS' Satellites (Altitude = 20,000 km)
Velocity = 3888 m/s SR time dilations = +7.26 E-6 seconds/day
GR time dilations = -4.557 E-5 seconds/day
Net time dilation = -38.4 micro seconds/day
----------------------------------------------------------------------------
So if that is true then:
clocks in LOW earth orbit go over 20 micro seconds/day SLOW
whereas
clocks in HIGH earth orbit go nearly 40 micro seconds/day FAST.
And i wouldn't have thought a clock would even know what orbit
it was in eh!
keith stein
.
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| User: "Jan Panteltje" |
|
| Title: Re: The facts about GPS and GR |
21 Dec 2003 07:49:48 AM |
|
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On a sunny day (Sun, 21 Dec 2003 10:00:33 -0000) it happened "Keith Stein"
<ks012a2355@blueyonder.co.uk> wrote in
<GaeFb.1973$uH5.1552@news-binary.blueyonder.co.uk>:
The following simple basic program shows how the time dilations on
satellites are worked out. Even if you are not a computer programmer
you should find you can understand this, that's the nice thing about
BASIC eh!
==================================================
PRINT "This program gives the SR and GR predicted time-dilations for"
PRINT "an Earth Satelite in a circular orbit, at any given altitude."
PRINT
REM VALUES OF THE PHYSICAL CONSTANTS USED
c = 2.99792E+08
G = 6.67259E-11
m = 5.976E+24
R = 6378000
DO: REM prompt user for 'ALTITUDE OF SATALITE'
:-); I presume U mean Santalite?
Good thing you gave the answer, nobody has BASIC anymore perhasp.
.
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| User: "Jeff Relf" |
|
| Title: Re: The facts about GPS and GR |
19 Dec 2003 04:40:27 PM |
|
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Hello Tom Potter , You wrote ,
" There have been many posts
asserting that General Relativity
is essential to the GPS system "
No , Special and general relativity
are necessary to Understand the GPS system .
There's a big difference .
When Einstein was a clerk in Switzerland in 1905 ,
There was a lot of work going on
on how to synchronize clocks .
In away , Switzerland and not Einstein
should get much of the credit for
the theory behind today's GPS systems .
In away , Einstein was the world's greatest watchmaker .
As we can now use a Casio wristwatch to get
the current time ( in nanoseconds ) and position
anywhere near the surface of the earth .
And with Hawking's work
on the quantum qualities of black holes and the big bang ,
We know much more about " Cosmic time " .
( Which , metaphysically , I think of as the heatscape ,
the fifth spatial dimension into which gravity curves )
To locate an object ,
The GPS constellation requires exactly four dimensions .
No more . No less .
But , observationally , the GPS' gravitational fields ,
a.k.a. The Einsteinian spacetime ,
likely didn't exist before the big bang .
Nor will they likely exist after the big freeze .
The universe as we perceive it is likely to be progressing
from the infinitely hot Big Bang
to the infinitely cold Big Freeze .
So the universe seems to be progressing
not just through the Einsteinian timescape ,
but also though a " Heatscape " ...
Which might therefore be thought of as
the fifth spatial dimension .
So at 10 ^ -X seconds after the big bang ,
as X approaches infinity ,
the degrees Kelvin probably approaches infinity .
And at 10 ^ X years after the big bang ,
as X approaches infinity ,
the degrees Kelvin probably approaches zero .
.
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