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Topic: GPS accounts for Relativity Effects (Read 504 times) |
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Barukh
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GPS accounts for Relativity Effects
« on: Aug 26th, 2007, 11:55pm » |
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Did you know that GPS sattelites' clocks are adjusted to take into account both Special and General Relativity predictions?
Read here. There are also several much more technical articles on-line.
I have read in another place that without these, the whole system won't work reliably.
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| « Last Edit: Aug 26th, 2007, 11:56pm by Barukh » |
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towr
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Re: GPS accounts for Relativity Effects
« Reply #1 on: Aug 27th, 2007, 12:09am » |
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on Aug 26th, 2007, 11:55pm, Barukh wrote:| Did you know that GPS sattelites' clocks are adjusted to take into account both Special and General Relativity predictions? |
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Yes, they'd be off by kilometers a day if not for the adjustment. It's good everyday evidence for relativity theory; which some people would think so far removed from their reality that you have to take it purely on faith.
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Sameer
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Re: GPS accounts for Relativity Effects
« Reply #2 on: Aug 27th, 2007, 7:01pm » |
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Correct, the time/distance dilations calculated using these theories play an important part in correcting the values read.. GPS..radars, etc.
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JiNbOtAk
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Re: GPS accounts for Relativity Effects
« Reply #3 on: Aug 29th, 2007, 2:19am » |
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So, whats' the difference between Special and General Relativity ?
<Note : I could get the info off the net, but I prefer letting you guys do the explaination, which I had always find out to be very easy to understand for laymen like me>
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| « Last Edit: Aug 29th, 2007, 2:19am by JiNbOtAk » |
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rmsgrey
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Re: GPS accounts for Relativity Effects
« Reply #4 on: Aug 29th, 2007, 3:30am » |
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on Aug 29th, 2007, 2:19am, JiNbOtAk wrote:So, whats' the difference between Special and General Relativity ?
<Note : I could get the info off the net, but I prefer letting you guys do the explaination, which I had always find out to be very easy to understand for laymen like me> |
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Special Relativity is about physics at high (relative) speeds but ignores gravity and acceleration. General Relativity adds gravity and acceleration to that picture.
In the context of GPS, Special Relativity says there's a time-dilation effect making the satellites' clocks run slow because they're moving faster than we are on the ground. General Relativity adds a time-dilation making our clocks run slow because we're in a more intense gravitational field. If memory serves, the SR effect is roughly twice the GR effect, but I could well be wrong on that.
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JiNbOtAk
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Re: GPS accounts for Relativity Effects
« Reply #5 on: Aug 29th, 2007, 3:42am » |
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on Aug 29th, 2007, 3:30am, rmsgrey wrote:| Special Relativity is about physics at high (relative) speeds but ignores gravity and acceleration. General Relativity adds gravity and acceleration to that picture. |
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How high is high speeds ? And I assume the speed is constant, since we're ignoring gravity and acceleration ?
Why would we bother with Special Relativity anyway, since General Relativity is the more accurate one ?
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Barukh
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Re: GPS accounts for Relativity Effects
« Reply #6 on: Aug 29th, 2007, 4:42am » |
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on Aug 29th, 2007, 3:42am, JiNbOtAk wrote:How high is high speeds ? And I assume the speed is constant, since we're ignoring gravity and acceleration ?
Why would we bother with Special Relativity anyway, since General Relativity is the more accurate one ? |
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The following excerpt taken from here :
"Accurate navigation with the GPS is made possible by the phenomenal performance of modern atomic clocks. If navigation errors of more than a meter are to be avoided, an atomic clock must deviate by less than about 4 nanoseconds from perfect synchronization with the other satellite clocks. That amounts to a fractional time stability of better than a part in 1013 . Only atomic clocks can do that. Even so, the system requires frequent uploads of clock corrections to the satellites.
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Relativistic effects are much larger than a part in 1013. For example, satellite speeds are about 4 km/s. Time dilation then causes the moving clocks' frequencies to be slow by v2/2c2 = 10-10. Gravitational effects are even larger. In fact, relativistic effects are about 10 000 times too large to ignore".
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towr
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Re: GPS accounts for Relativity Effects
« Reply #7 on: Aug 29th, 2007, 6:02am » |
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on Aug 29th, 2007, 3:30am, rmsgrey wrote:| If memory serves, the SR effect is roughly twice the GR effect, but I could well be wrong on that. |
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From http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity
"For the GPS satellites, general relativity predicts that the atomic clocks at GPS orbital altitudes will tick more rapidly, by about 45,900 nanoseconds (ns) per day, because they are in a weaker gravitational field than atomic clocks on Earth's surface. Special relativity predicts that atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by about 7,200 ns per day. When combined, the discrepancy is 38 microseconds per day"
So the GR effect is about 6 times the SR effect.
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towr
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Re: GPS accounts for Relativity Effects
« Reply #8 on: Aug 29th, 2007, 6:09am » |
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on Aug 29th, 2007, 3:42am, JiNbOtAk wrote:Special relativity applies at any speed, but for low speed it doesn't give noticibly different results then newtonian physics.
For timedilation you have
tobj= t0 * sqrt(1 - (v/c)2)
Where c is the speed of light, and v is the speed of the object
And since the speed of light is very larger, (v/c)2 is often practically 0 (And so the object practically experience the same time as non-moving object)
Quote:| Why would we bother with Special Relativity anyway, since General Relativity is the more accurate one ? |
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I'm not sure general relativity encompasses special relativity.
In any case, if it did, we would still use it for the same reason we still use newtonian physics, it's much simpler in cases where it can safely be applied.
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