Timeline for Why isn't the GPS location calculated from the Schwarzschild metric?
Current License: CC BY-SA 4.0
24 events
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| Nov 22, 2018 at 2:10 | comment | added | user71659 | @IlmariKaronen cm-scale GPS receiver systems do exist, but fundamentally they operate based on measuring the signal at reference locations and then sending out a correction, either with a time error (pseudorange) or position error. This is known as dGPS and many systems exist (WAAS/SBAS, LAAS/GLS, Starfire, SAIF, etc). Therefore, there is no need to make a special correction for every single possible error source, instead measuring error on a per-satellite or per-location basis. | |
| Nov 22, 2018 at 1:31 | comment | added | hmakholm left over Monica | The general-relativistic correction to the satellites' clock rates is not a matter of "imperfect clocks" -- gravitational time dilation is straight from GR. But it's not something GPS receivers need to care about, because the signal is already corrected for it when it is generated on the satellite. | |
| Nov 22, 2018 at 0:44 | comment | added | Mars | @IlmariKaronen I believe those GPS systems are likely using other augments already--a typical cell phone GPS is supposedly has an accuracy of around 4.9m under open sky (according to gps.gov). Order of magnitude doesn't change though | |
| S Nov 21, 2018 at 23:49 | history | suggested | user2357112 | CC BY-SA 4.0 |
That's the radius of the orbit, not the radius of the satellite. We are nowhere near the point of being able to put megameter-scale objects in orbit.
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| Nov 21, 2018 at 23:47 | review | Suggested edits | |||
| S Nov 21, 2018 at 23:49 | |||||
| Nov 21, 2018 at 23:13 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 22:48 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 22:33 | comment | added | G. Smith | I agree. That's why my first sentence said "The general-relativistic corrections are too small to matter" and later I explained that "This is below the accuracy of the GPS system." @hobbs arleady mentioned "imperfect clocks" and four other sources of inaccuracy greater than the GR corrections. | |
| Nov 21, 2018 at 22:28 | comment | added | Chris♦ | To be clear, this specific general relativistic correction is too small to matter. The clock drift that would occur without general relativistic corrections is much more significant. | |
| Nov 21, 2018 at 22:02 | comment | added | G. Smith | Thank you for accepting the answer despite my mistake. | |
| Nov 21, 2018 at 22:02 | comment | added | G. Smith | I've appended a correction to my answer. | |
| Nov 21, 2018 at 22:02 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 21:51 | comment | added | G. Smith | Whoops. Thank you for pointing out that I used the incorrect satellite radius. | |
| Nov 21, 2018 at 20:49 | comment | added | label | Just a minor correction: the orbital radius of satellites is (according to wiki) approximately 26600km, so 20000km is the altitude. This obviously doesn't affect the argument nor the order of magnitude of the calculated quantities. | |
| Nov 21, 2018 at 20:17 | comment | added | label | Thank you for the thorough answer. It's quite a surprise to me that the spacetime of the orbiting satellite can be considered to be Minkowski on such a large scale. The Earth's gravity really is weak. | |
| Nov 21, 2018 at 20:01 | vote | accept | label | ||
| Nov 21, 2018 at 18:50 | comment | added | G. Smith | I would appreciate it if ‘label’ accepted my answer, since I spent a lot of time on it, | |
| Nov 21, 2018 at 18:46 | comment | added | Ilmari Karonen | What's surprising to me is not that the effect is insignificant, but how close it is to being significant. A decent commercial GPS receiver can be accurate to less than one meter under good conditions, so an error of 1 cm due to GR is only two orders of magnitude below that. I can easily imagine a future GPS-like system being accurate enough for those corrections to be needed. | |
| Nov 21, 2018 at 15:55 | comment | added | hobbs | For comparison, the errors on any individual pseudorange due to signal resolution, ionospheric effects, thermal noise, imperfect clocks on the satellites, imperfect ephemerides, etc. under good conditions are around 10 nanoseconds, ~30 times larger. | |
| Nov 21, 2018 at 8:55 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 6:43 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 6:35 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 5:01 | history | edited | G. Smith | CC BY-SA 4.0 |
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| Nov 21, 2018 at 4:56 | history | answered | G. Smith | CC BY-SA 4.0 |