some numbers to put it into perspective
1) clocks at GPS orbital altitudes will tick faster by about 45,900 ns/day
2) clocks moving at GPS orbital
speeds will tick slower by about 7,200 ns/day
3) clocks adjusted before launch to these numbers, resulting no more than +/-
200 ns/day error
(1 ns = 1 foot)
4) gravitational lensing is not an issue, and there is no difference in the
speed of light in any direction from an observer (GPS related)
5) there is some curving of the RF signal due to air density changes, ground
users can ignore it.
6) accuracy of the orbital position of each satellite is the major component of
the solution accuracy. Satellites do not fly in perfect, repetitive circle.
For example the pressure of the sunlight is a very observable effect....
To get "extreme" accuracy, down to a couple of centimeters, is not done in real
time. It takes inputs from many different sources and long computations. But
it is very satisfactory when the ground observations match the GPS solutions...
Leslie.
________________________________
From: "dre...@gmail.com" <dre...@gmail.com>
To: cnc-list@cnc-list.com
Sent: Tuesday, January 29, 2013 7:04 AM
Subject: Re: Stus-List More on GPS accuracy & Einstein
Hi,
While we are chatting about how GPS works and its accuracy, I would like add a
few interesting tidbits.
A good part of the accuracy come from taking Einstein's Relativity into
account. Special Relativistic effects like properly calculating doppler shifts
and relative motion are important, but also General Relativistic effects need
to be applied. For example, Special Relativity states that moving clocks run
slower, but General Relativity states that clocks run slower in a gravitational
field. Satellites are moving fast compared to someone on Earth so this makes
their clocks to run slower. But satellites feel less of the earth's gravity so
our Earth-bound clocks run slower. Since a satellite speed, while fast to us
is slow relative to the speed of light, our Earthly clocks end up running
slower than clocks on GPS satellites (~50 microseconds/day which amounts to
about a 7 nautical mile spread!). Also, light (i.e. GPS signals) do not travel
in a straight path as one assumes in triangulating a "fix". Rather matter
curves space around it, so
GPS signals actually bend (i.e. gravitational lensing). The latter effect,
which is tiny compared to the former, was actually proved using a sextant of
sort, by measuring a star's position during a solar eclipse in 1919.
While these effects are ordinarily insignificant for life on Earth, they are
important on the scale of GPS accuracy. I am sure that Einstein did not have
GPS in mind when he wrote down the theory of Relativity, but I'll still thank
him nonetheless.
-
Paul E.
1979 C&C 29 Mk1
S/V Johanna Rose
Carrabelle, FL
On Jan 29, 2013, at 8:44 AM, cnc-list-requ...@cnc-list.com wrote:
Message: 5
>Date: Tue, 29 Jan 2013 05:55:03 +0000
>From: "Brent Driedger" <bren...@highspeedcrow.ca>
>To: "Leslie Paal" <lpaalc...@yahoo.com>, cnc-list@cnc-list.com
>Subject: Re: Stus-List More on GPS accuracy
>Message-ID:
><499177535-1359438905-cardhu_decombobulator_blackberry.rim.net-1984730907-@b17.c8.bise6.blackberry>
>
>Content-Type: text/plain; charset="Windows-1252"
>
>I'm enjoying this in depth GPS education.
>I recall some scuttlebutt in Sail magazine a year or two ago warning that most
>of the birds in the system were approaching their "best before date" of over
>25 years and without getting immediate replacement the system would be down a
>few leaving some holes or temporary signal loss in some locations in the
>coming years. Have you heard any updates to this rumor?
>
>Brent Driedger
>s/v Wild Rover
>C&C 27-5
>Sent from my BlackBerry? smartphone on the MTS High Speed Mobility Network
>
>-----Original Message-----
>From: Leslie Paal <lpaalc...@yahoo.com>
>Sender: "CnC-List" <cnc-list-boun...@cnc-list.com>
>Date: Mon, 28 Jan 2013 12:04:01
>To: cnc-list@cnc-list.com<cnc-list@cnc-list.com>
>Reply-To: Leslie Paal <lpaalc...@yahoo.com>, cnc-list@cnc-list.com
>Subject: Stus-List More on GPS accuracy
>
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