Equation: How GPS Bends Time

[div class=attrib]From Wired:[end-div]

Einstein knew what he was talking about with that relativity stuff. For proof, just look at your GPS. The global positioning system relies on 24 satellites that transmit time-stamped information on where they are. Your GPS unit registers the exact time at which it receives that information from each satellite and then calculates how long it took for the individual signals to arrive. By multiplying the elapsed time by the speed of light, it can figure out how far it is from each satellite, compare those distances, and calculate its own position.

For accuracy to within a few meters, the satellites’ atomic clocks have to be extremely precise—plus or minus 10 nanoseconds. Here’s where things get weird: Those amazingly accurate clocks never seem to run quite right. One second as measured on the satellite never matches a second as measured on Earth—just as Einstein predicted.

According to Einstein’s special theory of relativity, a clock that’s traveling fast will appear to run slowly from the perspective of someone standing still. Satellites move at about 9,000 mph—enough to make their onboard clocks slow down by 8 microseconds per day from the perspective of a GPS gadget and totally screw up the location data. To counter this effect, the GPS system adjusts the time it gets from the satellites by using the equation here. (Don’t even get us started on the impact of general relativity.)

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22 thoughts on “Equation: How GPS Bends Time”

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