# The Naked Scientists Forum

### Author Topic: GPS & relativity  (Read 6969 times)

#### DoctorBeaver

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##### GPS & relativity
« on: 26/06/2007 15:03:39 »
Do you realise that GPS systems have to take relativity into account?

It's all because of the speed at which the signals travel (the speed of light). At those speeds, relativistic effects must be factored into the calculations. If they are ignored, errors can accumulate at the rate of 10km per day!

So, next time your GPS successfully takes you from A to B, and not into the nearest canal, say a quick thank you to uncle Albert.

#### Bored chemist

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##### GPS & relativity
« Reply #1 on: 27/06/2007 11:22:56 »
Ironically this also means that (when they were set up on earth) some of the most expensive clocks in history were set to run wrongly.

#### DoctorBeaver

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##### GPS & relativity
« Reply #2 on: 28/06/2007 07:05:35 »
Oooh, thanks. You've given me a good excuse for being late!

#### daveshorts

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##### GPS & relativity
« Reply #3 on: 28/06/2007 09:26:59 »
I don't think it is so much the speed that the signals travel which mean you have relativistic effects but that you are increadibly sensitive to tiny changes in clocks. You are measuring your position using light which goes at 300000km/s so to get a 10km error you only need a 30μs error.

The relativistic effects come in because your clocks are flying around at 7-8km/s and are being accelerated by gravity slightly differently than someone standing on earth. This is far smaller than the speed of light so the relativistic effects are minute, however the system is so sensitive to tiny time errors it is still an issue.

#### DoctorBeaver

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##### GPS & relativity
« Reply #4 on: 28/06/2007 14:46:10 »
Dave - you're quite right. It is the relativistic effects of gravity on the photons that causes the error. I merely tried to simplify it.

#### JimBob

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##### GPS & relativity
« Reply #5 on: 28/06/2007 23:18:02 »
There is also the problem of getting the right UTM coordinate system - Universal Transverse Mercator zone.

There are 60 of them and several different projection systems. In the US the two the NAD 27 and 83. England has the European Datum 1950, European Datum 1979, Ordnance Survey 1936, Ireland 1965

The French need 2 - The NTF France (Greenwich Meridian) and NTF France (Paris Meridian.)

SO I guess it depends on which one your GPS is set to or which one you select. It makes a difference of many feet to 100's of feet, if you are on the edge of the projection area.

Uncle Albert never counted on bureaucrats !!!!

#### daveshorts

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##### GPS & relativity
« Reply #6 on: 29/06/2007 09:13:21 »
I was once driving a boat near Rodes and we were plotting our position on an old chart, which seemed to put us 1km inland as we motored all the way up the side of the island, because of this sort of problem...

#### safertr

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##### GPS & relativity
« Reply #7 on: 05/07/2007 14:56:38 »
People often ask me "What good is Relativity?" It is a commonplace to think of Relativity as an abstract and highly arcane mathematical theory that has no consequences for everyday life. This is in fact far from the truth.

Consider for a moment that when you are riding in a commercial airliner, the pilot and crew are navigating to your destination with the aid of the Global Positioning System (GPS). Further, many luxury cars now come with built-in navigation systems that include GPS receivers with digital maps, and you can purchase hand-held GPS navigation units that will give you your position on the Earth (latitude, longitude, and altitude) to an accuracy of 5 to 10 meters that weigh only a few ounces and cost around \$100.

GPS was developed by the United States Department of Defense to provide a satellite-based navigation system for the U.S. military. It was later put under joint DoD and Department of Transportation control to provide for both military and civilian navigation uses.

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.

#### Bored chemist

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##### GPS & relativity
« Reply #8 on: 05/07/2007 20:05:38 »
The clocks are in free fall whereas earth bound clocks are affected by gravity; this makes another correction neccessary.
I still remember someone telling me about a group of hill walkers standing next to an OS triangulation point looking at their new GPS system and saying "according to this, we are about 100 yards over that way".
Don't forget that once GPS technology gets accuracy better than about 10cm you will need to take account of which pocket you put it in.

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##### GPS & relativity
« Reply #9 on: 05/07/2007 20:55:24 »
The domestic GPS system we are "allowed" to use is different in quality to the military system, the accuracy of the military GPS is about 30cm and the domestic GPS about 15M.

I think it doubtful that the domestic system will improve much in quality because of the terrorist implications as it is already possible to use a more accurate system and has been for a while but, its reserved for the Military.

Edit: Just read that it was meant to be changed in 2000, but whether we get the full version now is debatable as it can be degraded at any time.

Cruise missiles rounding street corners in Iraq cities and going through windows shows how accurate and devastating it can be!

There was an interesting incident a few years ago regarding 2 military satellites that suddenly dipped in orbit and had to be repositioned. The satellites were checked out and nothing was found to be wrong. Nasa has still not been able to state why but gave a few possible reasons: It could be due to relativity and a possible frame dragging effect or that our model of Gravity is wrong somewhere.

There is still no explanation and so far it has not occurred again.

I have had difficulty in the past (several months ago) trying to find out any information as the Gravity and Relativistic effects interest me.

Bee

« Last Edit: 05/07/2007 21:10:50 by that mad man »

#### The Naked Scientists Forum

##### GPS & relativity
« Reply #9 on: 05/07/2007 20:55:24 »