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        riddles >> general problem-solving / chatting / whatever >> GPS accounts for Relativity Effects
        
(Message started by: Barukh on Aug 26^th, 2007, 11:55pm)

Title: GPS accounts for Relativity Effects
Post by Barukh on Aug 26^th, 2007, 11:55pm

Did you know that GPS sattelites' clocks are adjusted to take into account both Special and General Relativity predictions?

Read here (http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity). 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.

:o

Title: Re: GPS accounts for Relativity Effects
Post by towr on Aug 27^th, 2007, 12:09am

on 08/26/07 at 23:55:03, Barukh wrote:

Did you know that GPS sattelites' clocks are adjusted to take into account both Special and General Relativity predictions?

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.

Title: Re: GPS accounts for Relativity Effects
Post by Sameer on Aug 27^th, 2007, 7:01pm

Correct, the time/distance dilations calculated using these theories play an important part in correcting the values read.. GPS..radars, etc.

Title: Re: GPS accounts for Relativity Effects
Post by JiNbOtAk on Aug 29^th, 2007, 2:19am

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>

Title: Re: GPS accounts for Relativity Effects
Post by rmsgrey on Aug 29^th, 2007, 3:30am

on 08/29/07 at 02:19:03, JiNbOtAk wrote:

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.

Title: Re: GPS accounts for Relativity Effects
Post by JiNbOtAk on Aug 29^th, 2007, 3:42am

on 08/29/07 at 03:30:21, 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.

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 ?

Title: Re: GPS accounts for Relativity Effects
Post by Barukh on Aug 29^th, 2007, 4:42am

on 08/29/07 at 03:42:41, JiNbOtAk wrote:

The following excerpt taken from here (http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf):

"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.
...
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".

Title: Re: GPS accounts for Relativity Effects
Post by towr on Aug 29^th, 2007, 6:02am

on 08/29/07 at 03:30:21, rmsgrey wrote:

If memory serves, the SR effect is roughly twice the GR effect, but I could well be wrong on that.

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.

Title: Re: GPS accounts for Relativity Effects
Post by towr on Aug 29^th, 2007, 6:09am

on 08/29/07 at 03:42:41, JiNbOtAk wrote:

How high is high speeds?

Special relativity applies at any speed, but for low speed it doesn't give noticibly different results then newtonian physics.

For timedilation you have
t_obj= 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 ?

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.