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GPS - Relativity can be ignored...

 Posts: 1,919 Add as FriendChallenge to a DebateSend a Message 3/11/2016 2:18:38 PMPosted: 1 year agoAt least insofar as establishing a geographical position anyway, here's why.Atomic clocks launched from earth and placed into orbit at 20,200 km will "tick" more rapidly than their earthbound counterparts - this discrepancy seems to be that they gain 38 uS every 24 hours.To compensate these clocks are adjusted to lose 38 uS per day and so once in orbit they more or less "tick" at the same rate and keep track with GMT (they are also periodically corrected by tiny amounts).If a radio signal is sent from such a satellite it will take about 67 mS to reach the earth (speed_of_light / satellite_altitude_in_m).So the question arises - how much error would we see between a earthbound clock and a orbiting clock that had been uncompensated?Well we know it gains 38 uS every 24 hours or 38 uS every 864,000,000,000 uS.This equates to 38 uS every 864,000,000 mS.Therefore such an orbiting clock would gain (67 / 864,000,000) * 38 uS which is a very small number, in fact it amounts to around 3 pS (which is 10-12 of a second).Well high quality GPS receivers have time resolutions around 15 nS so 3 pS is far below what could even be detected by a receiver, in fact the 3 pS represents and error to such a clock of around (3 / 15,000) = 0.02% of the receivers own resolution.These simple calculations seem to show that despite orbiting clocks ticking more rapidly due to relativistic effects, the significance of this on a per-time signal basis is irrelevant.In fact 3 pS at the speed of light amounts to a distance of around 0.8 mm !!So Dummel please tell me if you agree or disagree with these calculations and if you disagree where have I erred?Harry.
 Posts: 4,982 Add as FriendChallenge to a DebateSend a Message 3/11/2016 2:43:07 PMPosted: 1 year agoAt 3/11/2016 2:18:38 PM, Dirty.Harry wrote:At least insofar as establishing a geographical position anyway, here's why.Atomic clocks launched from earth and placed into orbit at 20,200 km will "tick" more rapidly than their earthbound counterparts - this discrepancy seems to be that they gain 38 uS every 24 hours.To compensate these clocks are adjusted to lose 38 uS per day and so once in orbit they more or less "tick" at the same rate and keep track with GMT (they are also periodically corrected by tiny amounts).If a radio signal is sent from such a satellite it will take about 67 mS to reach the earth (speed_of_light / satellite_altitude_in_m).So the question arises - how much error would we see between a earthbound clock and a orbiting clock that had been uncompensated?Well we know it gains 38 uS every 24 hours or 38 uS every 864,000,000,000 uS.This equates to 38 uS every 864,000,000 mS.Therefore such an orbiting clock would gain (67 / 864,000,000) * 38 uS which is a very small number, in fact it amounts to around 3 pS (which is 10-12 of a second).Well high quality GPS receivers have time resolutions around 15 nS so 3 pS is far below what could even be detected by a receiver, in fact the 3 pS represents and error to such a clock of around (3 / 15,000) = 0.02% of the receivers own resolution.These simple calculations seem to show that despite orbiting clocks ticking more rapidly due to relativistic effects, the significance of this on a per-time signal basis is irrelevant.In fact 3 pS at the speed of light amounts to a distance of around 0.8 mm !!So Dummel please tell me if you agree or disagree with these calculations and if you disagree where have I erred?Harry.And on day 2?
 Posts: 548 Add as FriendChallenge to a DebateSend a Message 3/11/2016 3:56:44 PMPosted: 1 year agoAt 3/11/2016 2:18:38 PM, Dirty.Harry wrote:At least insofar as establishing a geographical position anyway, here's why.Atomic clocks launched from earth and placed into orbit at 20,200 km will "tick" more rapidly than their earthbound counterparts - this discrepancy seems to be that they gain 38 uS every 24 hours.To compensate these clocks are adjusted to lose 38 uS per day and so once in orbit they more or less "tick" at the same rate and keep track with GMT (they are also periodically corrected by tiny amounts).If a radio signal is sent from such a satellite it will take about 67 mS to reach the earth (speed_of_light / satellite_altitude_in_m).So the question arises - how much error would we see between a earthbound clock and a orbiting clock that had been uncompensated?Well we know it gains 38 uS every 24 hours or 38 uS every 864,000,000,000 uS.This equates to 38 uS every 864,000,000 mS.Therefore such an orbiting clock would gain (67 / 864,000,000) * 38 uS which is a very small number, in fact it amounts to around 3 pS (which is 10-12 of a second).It is not the time dilation during a transmission that is important. It is the fact that 24hrs later this clock is 38us wrong, which is a potential distance error of 11400m. If this went uncorrected the system is useless. As you say this correction is mostly done by making a clock than runs slightly slow, but it must be done.Well high quality GPS receivers have time resolutions around 15 nS so 3 pS is far below what could even be detected by a receiver, in fact the 3 pS represents and error to such a clock of around (3 / 15,000) = 0.02% of the receivers own resolution.These simple calculations seem to show that despite orbiting clocks ticking more rapidly due to relativistic effects, the significance of this on a per-time signal basis is irrelevant.In fact 3 pS at the speed of light amounts to a distance of around 0.8 mm !!So Dummel please tell me if you agree or disagree with these calculations and if you disagree where have I erred?Harry.Let's hope "the truth is out there" cos there is bugger all round here.
 Posts: 1,919 Add as FriendChallenge to a DebateSend a Message 3/11/2016 4:04:37 PMPosted: 1 year agoAt 3/11/2016 2:43:07 PM, Ramshutu wrote:At 3/11/2016 2:18:38 PM, Dirty.Harry wrote:At least insofar as establishing a geographical position anyway, here's why.Atomic clocks launched from earth and placed into orbit at 20,200 km will "tick" more rapidly than their earthbound counterparts - this discrepancy seems to be that they gain 38 uS every 24 hours.To compensate these clocks are adjusted to lose 38 uS per day and so once in orbit they more or less "tick" at the same rate and keep track with GMT (they are also periodically corrected by tiny amounts).If a radio signal is sent from such a satellite it will take about 67 mS to reach the earth (speed_of_light / satellite_altitude_in_m).So the question arises - how much error would we see between a earthbound clock and a orbiting clock that had been uncompensated?Well we know it gains 38 uS every 24 hours or 38 uS every 864,000,000,000 uS.This equates to 38 uS every 864,000,000 mS.Therefore such an orbiting clock would gain (67 / 864,000,000) * 38 uS which is a very small number, in fact it amounts to around 3 pS (which is 10-12 of a second).Well high quality GPS receivers have time resolutions around 15 nS so 3 pS is far below what could even be detected by a receiver, in fact the 3 pS represents and error to such a clock of around (3 / 15,000) = 0.02% of the receivers own resolution.These simple calculations seem to show that despite orbiting clocks ticking more rapidly due to relativistic effects, the significance of this on a per-time signal basis is irrelevant.In fact 3 pS at the speed of light amounts to a distance of around 0.8 mm !!So Dummel please tell me if you agree or disagree with these calculations and if you disagree where have I erred?Harry.And on day 2?Day number doesn't play a role in any of the above calculations.Harry.
 Posts: 1,919 Add as FriendChallenge to a DebateSend a Message 3/12/2016 3:56:43 PMPosted: 1 year agoJust imagine you have a stopwatch that you KNOW gains a second every minute.Well can we use that to measure an athlete's speed?Do we need to know what time it is in order to measure that speed?Harry.