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Re^6: Converting GPS seconds to readable time&date (relativity)
by zentara (Cardinal) on Jan 12, 2009 at 12:14 UTC
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I guess you are right. Since the GPS satellites are geo-stationary, we move faster on earth, as opposed to normal satellites. There I go thinking again. :-)
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That can't be right. The circumference of a geostationary orbit is much larger than the circumference of a ground level orbit, so that means the satellites must be moving much faster than someone on Earth to move in sync.
groud level orbit = 0.46 km/s
geostationary orbit = 3.07 km/s
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The satellites "move faster" according to one frame of reference, but the point of relativity is that the answers are independent of frame of reference. From the satellite's point of view, we are moving more than they are.
The important thing is that satellites feel no acceleration. They are just floating (in orbit). Those of us "who are stuck in the muck of earth's gravity" feel about 1g of acceleration all of the time, and this slows down the passage of time for us.
If I jump into a space ship and fly far away at near the speed of light and then return at near the speed of light, I will have aged less than y'all. And I will have felt a lot of acceleration in getting up to speed and then in changing direction.
I was just reading "The Elegant Universe" and thought it got parts of the explanation of relativity wrong. But I eventually realized that most of the explanations I'd heard before got it wrong. The key point that prior explanations missed is that if you are moving relative to me, then it is quite complicated to compare our clocks accurately, since the time it takes signals to pass between us keeps changing. According to relativity, if we are both "coasting" but moving relative to each other, there really is no answer to "whose clock is running faster". You can look at things different ways and get different answers to that question, and each of those different answers is equally valid.
But if we move apart and then move back together again, then we can precisely compare how much time has passed on our different clocks. And the clock that has aged the least will be the one that experienced the most acceleration (as I currently understand things).
No, I'm not an expert on relativity, so I easily admit that I could have made any number of errors above.
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I finally came across this which seems quite authoratative with some interesting graphs and stuff about the various factors that affect GPS accuracy. The final section on the page: "Relativistic effects" is worth quoting verbatim rather than attempting to paraphrase (and get it wrong):
As we already learned, the time is a relevant factor in GPS navigation and must be accurate to 20 - 30 nanoseconds to ensure the necessary accuracy. Therefore the fast movement of the satellites themselves (nearly 12000 km/h) must be considered.
Whoever already dealt with the theory of relativity knows that time runs slower during very fast movements. For satellites moving with a speed of 3874 m/s, clocks run slower when viewed from earth. This relativistic time dilation leads to an inaccuracy of time of approximately 7,2 microseconds per day (1 microsecond = 10-6 seconds).
The theory of relativity also says that time moves the slower the stronger the field of gravitation is. For an observer on the earth surface the clock on board of a satellite is running faster (as the satellite in 20000 km height is exposed to a much weaker field of gravitation than the observer). And this second effect is six times stronger than the time dilation explained above.
Altogether, the clocks of the satellites seem to run a little faster. The shift of time to the observer on earth would be about 38 milliseconds per day and would make up for an total error of approximately 10 km per day. In order that those error do not have to be corrected constantly, the clocks of the satellites were set to 10.229999995453 Mhz instead of 10.23 Mhz but they are operated as if they had 10.23 MHz. By this trick the relativistic effects are compensated once and for all.
There is another relativistic effect, which is not considered for normal position determinations by GPS. It is called Sagnac-Effect and is caused by the movement of the observer on the earth surface, who also moves with a velocity of up to 500 m/s (at the equator) due to the rotation of the globe. The influence of this effect is very small and complicate to calculate as it depends on the directions of the movement. Therefore it is only considered in special cases.
Which shows that everything is relative, including (my) understanding :)
The final solution to all the relativistic affects (except the last), running the on-board clock a little slow but treating its output if it was running at the 'right' speed, is so incredibly simple it beggars belief.
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
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GPS satellites are geo-stationary, they are in MEO
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GPS satellites arent geo-stationary, they are in MEO
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