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Topic: The power of basic science
Replies: 2   Last Post: Mar 25, 2013 5:51 AM

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Tom Potter

Posts: 497
Registered: 8/9/06
Re: The power of basic science
Posted: Mar 25, 2013 5:51 AM
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"Wally W." <ww84wa@aim.com> wrote in message
news:1ivuk8tdobvsvu363qoiaes11efacclsgm@4ax.com...
> On Sun, 24 Mar 2013 20:02:16 -0000, jimp@specsol.spam.sux.com wrote:
>

>>Sam Wormley <swormley1@gmail.com> wrote:
>>> On 3/24/13 12:04 PM, jimp@specsol.spam.sux.com wrote:
>>>> Sam Wormley <swormley1@gmail.com> wrote:
>>>>> On 3/23/13 9:15 PM, jimp@specsol.spam.sux.com wrote:
>>>>
>>>>>> For lasers it was 1917 and for GPS it was around 1878.
>>>>>>

>>>>>
>>>>> Thanks be to Albert Einstein.

>>>>
>>>> For what?
>>>>
>>>> Nothing Einstein did is necessary to build either.
>>>>
>>>> Building a laser is pretty trivial once one is aware of the effect and
>>>> there are natural lasers.
>>>>
>>>> Absent Einstein the corrections needed to keep GPS accurate could have
>>>> been determined empirically.
>>>>

>>>
>>> Many don't understand the relativistic correction, jimp. There is no
>>> shame in that. See:

>>
>>You are changing the subject, ass hat.

>
> SOP for warmophobes.
>
> The news media doesn't notice because their attention span is only 8
> seconds long.
>

>>The relativistic correction has nothing to do with lasers.
>>
>>The relativistic correction is nothing more than a set of equations
>>that with enough data could be determined empirically.
>>
>>Does the phrase "curve fitting" mean anything to you ass hat.
>>
>>Granted such does not give a theoretical explaination of WHY it is so, but
>>it does give a working solution to build a system.


It is sad that most people have been brainwashed
to believe that General Relativity is a powerful model
and was and is essential to the GPS system.

The GPS system engineers designed
a ***closed loop system***
that adjusts for all possible effects including
the DOPPLER <velocity> EFFECT,
and the GALILEO <acceleration> EFFECT.

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.

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.

( The adjustments are not actually made to the clocks
and the oscillators that drive the clocks
but data is sent to each satellite
that it in turn transmits to GPS receivers
informing them what offsets must be applied to
correct that satellite's data to the master ground data.)

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
reference.

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.

Frankly the usefullness of the "precision code" is vastly overrated
as modern GPS receivers have the capacity to
phase lock with the carrier frequency.

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.

In order to identify each satellite,
and to measure the time interval most accurately,
a "quasi-random code" is used.

Part of the code includes a "Gold Code"
with good correlation properties.
and part of the code includes the satellite ID
and the data.

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.,

and to delineated the signal,
GPS receivers perform
an auto-correlation on the signal.

A segment of the quasi-random signal is
incrementally delayed, and multiplied by the signal stream.

If two strings of random numbers are multiplied,
a maximum occurs when and if the strings match,
otherwise the product tends toward zero.

After the signal is delineated using "auto-correlation",

it is further delineated by "cross-correlating"
the delineated blocks with the quasi-random codes
used to identify the satellites,

and the data associated with each satellite.
can thus be identified and decoded.

In summary, the largest contributor
to time transfer uncertainty is caused by
variations in path delay, due to signals reflected
off mountains, buildings, etc., and as noted,
much of the path delay errors can be averaged out,
because the satellites are moving, and signals
are received from several satellites.

The accuracy of the GPS system is limited mainly
by the random, non-homogenity of the air.

The best GPS receivers can,
by using the methods described above,
reduce the uncertainty in time to about one nanosecond,
which amounts to a sphere of uncertainty of about one foot.

--
Tom Potter

http://the-cloud-machine.tk
http://tiny.im/390k







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