Satellites, Smartphones and the Science of GPS


SiS is proud to feature the winners of the "2013 Driskill Graduate Program in the Life Sciences (DGP) Science and Society Class Distinction Award." Written as part of a course on science and society, these papers were chosen by DGP faculty to be published on SiS. This month, we present the following piece by PhD student Andrew Shum.

In September of 2012, Apple updated all of its iPhones to replace Google Maps with its own version of the application, Apple Maps. The update caused outrage in the vast community of iPhone users with complaints ranging from improper labeling of famous structures, such as the Washington Monument, to misleading directions through nonexistent roads. In one instance, several motorists in Australia used Apple Maps to locate the rural town of Mildura but were instead misled to a national park 37 miles away, a hostile environment with scorching hot temperatures of up to 115 F and no water supply.

This unfortunate incident highlights our society’s dependence on global positioning system (GPS) for everyday life, such as getting directions home or finding the nearest coffee shop. We take GPS for granted not realizing that its operation would not function properly had it not been for Albert Einstein and his famous theory of relativity.

In 1905, Einstein published his theory of special relativity, which stated that time is not constant, and that objects in motion experience time slower than objects at rest. His theory that time is a variable caused a paradigm shift in the field of physics and changed the way we view the natural world. He later followed up these ideas in 1916 when he published the theory of general relativity that included gravity’s effect on time. Objects on earth experience time slower than objects in space due to the relative effects of gravity.

These highly theoretical ideas were put to the test in 1971 when Joseph Hafele and Richard Keating placed extremely precise atomic clocks on commercial airliners and flew them around the world. Three clocks were synchronized on the ground: one was sent eastward, another sent westward, and then both were compared to the third clock left on the ground. The clocks all showed different values, but consistent with the theories of general and special relativity. In fact, the eastbound clock ran faster than the ground clock since it was traveling in the direction of Earth’s rotation. Conversely, the westbound clock was traveling against Earth’s rotation and was slower than the ground clock at a difference whose values are within 10 percent of the mathematically predicted values. However, these changes in time were extremely small, on the order of hundreds of nanoseconds.

So how can these incredibly small changes in time be applicable in the real world? Consider how GPS works. The global positioning systems depend on a constellation of 24 satellites that orbit 20,000 kilometers above the Earth’s surface. When you use a GPS device, such as your smartphone, to pinpoint your location, a signal is sent to one of those satellites. The time it takes for the signal to reach the satellite can be used to calculate the distance between it and the GPS device. Combining information from three different satellites can identify where the device is located within 5 to 10 meters in a matter of seconds. The accuracy of triangulating a GPS device’s location depends on a key factor: the clock on the device and the clocks on the satellites must be synchronized.

But, the satellites’ far distance from the Earth’s surface means that they experience less of an effect from gravity than any objects on Earth. Therefore, by the theory of general relativity, the satellites’ clocks move faster by 45 microseconds per day. Furthermore, the satellites orbit at high velocities of approximately 14,000 kilometers per second. Calculations using special relativity indicate that their clocks move slower by 7 microseconds per day. The net effect is that the satellites’ clocks will move 38 microseconds faster than clocks on Earth every 24 hours.

This time difference would translate into a farther distance than reality, leading to miscalculated locations. In just one day, the global positioning system’s 38 microseconds difference would cause an error of at least 10 kilometers making your GPS device tell you that you’re at LaGuardia Airport when you’re standing in Times Square. This error also accumulates if left unchecked. In order to correct for these relativistic changes in time, satellites are reprogrammed to tick at a slower frequency than normal clocks so that at their final orbit, they appear to tick synchronized with ground clocks. Finally, station clocks periodically check satellite clocks for aberrant changes in time, due to faster orbit speeds for example, and also maintain GPS device clocks since these are less accurate than expensive atomic clocks.

The implications of Einstein’s theory of relativity are absolutely astonishing. His ideas are still difficult concepts to grasp even 100 years after the theories were published. Despite the seemingly impossible idea that time is variable, many experiments, including those performed by Hafele and Keating, confirm that the relativistic time changes occur in reality and can be calculated mathematically with incredible accuracy. It would be interesting to imagine if Einstein had not existed and his theories never proposed, how these tiny inaccuracies would have been viewed. Even if the global positioning system existed, confused engineers would wonder why clocks on satellites never stayed precisely on time.

So every time you hit the pinpoint button on your iPhone, you demonstrate the application of Einstein’s theories of relativity to tell you where you are with incredible fidelity. Independent of this scientific and technological achievement, the fault of Apple Maps lies in its incomplete and erroneous map databases. Even with GPS, the accuracy of your location is rendered useless if your location is simply mislabeled. Apple has since apologized for the application's downfalls. But, when all else goes awry in your GPS device, you can rest assured knowing that the scientific basis of accurately calculating your navigational positions remains true.



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