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− | Could someone explain to me why a GPS wouldn’t work if relativity didn’t exist? {{unsigned ip|162.158.186.156}} | + | Could someone explain to me why a GPS wouldn’t work if relativity didn’t exist? |
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| :[http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html This is a good read.] [[Special:Contributions/172.69.210.28|172.69.210.28]] 06:43, 13 September 2018 (UTC) | | :[http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html This is a good read.] [[Special:Contributions/172.69.210.28|172.69.210.28]] 06:43, 13 September 2018 (UTC) |
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− | ::It is a good read. To summarize the main points of that article:
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− | ::* GPS satellites contain {{w|atomic clock}}s to keep time, and they broadcast their current time. A GPS receiver measures the amount of ''time'' it took for the signals to arrive from the satellites' known positions, using ''{{w|trilateration}}'' to determine the receiver's position. (This is different from ''{{w|triangulation}}'', which determines position by measuring ''angles''.)
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− | ::* GPS satellites orbit at a speed of 14,000 km/h relative to Earth's surface. One effect of this is {{w|Time dilation#Velocity time dilation|velocity time dilation}}: time passes ''slower'' for GPS satellites than it does near Earth's surface, drifting 7 microseconds ''behind'', every day.
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− | ::* GPS satellites orbit at an altitude of 20,000 km, which is far enough away from Earth's mass that {{w|spacetime}} curvature is different there. One effect of this is {{w|Time dilation#Gravitational time dilation|gravitational time dilation}}: time passes ''faster'' for GPS satellites than it does near Earth's surface, drifting 45 microseconds ''ahead'', every day.
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− | ::* Combining those, time passes faster for GPS satellites, by a net 38 ''microseconds'' (10<sup>-6</sup>) every day, relative to near Earth's surface.
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− | ::* But GPS precision depends on ''nanosecond''-range accuracy (10<sup>-9</sup>), so 38,000 nanoseconds drift would cause GPS precision to accumulate an ''additional 10 km of error every day''. GPS would still ''function'' – the satellites would still transmit, and the receivers would still calculate a position – but that position could be out by miles and miles; so if the purpose of GPS is to provide a reasonably precise position, then by that standard, GPS wouldn't ''work''.
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− | ::* {{w|Albert Einstein}}'s theories of {{w|special relativity}} and {{w|general relativity}} enable GPS to predict ''velocity time dilation'' and ''gravitational time dilation'' (respectively), and thereby compensate for the error so that GPS can ''work''!
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− | ::[[User:Yfmcpxpj|Yfmcpxpj]] ([[User talk:Yfmcpxpj|talk]]) 21:58, 5 September 2020 (UTC)
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− | :::I'm sorry, but to me, your summary seems to make it sound like relativity is a problem that we are correcting for, rather than enabling anything. If relativity didn't exist, we wouldn't need to correct for velocity and gravitational time dilation. Mind you, that's only what I get from your summary, haven't actually read the article.--[[Special:Contributions/172.68.94.150|172.68.94.150]] 22:35, 24 March 2023 (UTC)
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