|
How does satellite navigation work? It’s all Greek to me. Which, it is. Heron of Alexandria (10-70 AD) was a Greek mathematician who, besides inventing the steam engine, the syringe and the vending machine (seriously), also described a method for determining a triangle’s area from the length of its sides. Heron’s mathematical formula underpins a calculation called trilateration, which is itself the geometry behind the global positioning system, GPS
In fact, modern GPS was born from a British WWII technology called GEE navigation, in which night-time bomber raids over Germany were guided by radio signals broadcast from a chain of ground stations. Using an oscilloscope to find out the time, and therefore distance, from the stations, a bomber crew could work out their position without the need for a visual reference, and drop their payload on target.
After the war, the principle of hyperbolic navigation, using Heron’s trilateration formula, was further developed by the US – notably when US scientists were able to predict the location of Russia’s Sputnik satellite with greater precision than the Soviets could themselves.
|
It soon became apparent that reversing the concept – working out an unknown position of satellites – would also be useful in the Cold War; specifically, for nuclear submarines.
Todays GPS satellites circle the globe at 7000mph
Over the next 20 years the US military developed this GPS technology and built-up a supporting satellite network. By the early 1980s its applications were still exclusively military, but that changed in 1983 when the Soviets shot down a South Korean passenger airliner that had strayed into Russian airspace after a navigational error. US president Ronald Regan declared that, to avoid such tragedy again, the network of GPS satellites would be made available for civilian uses once complete.
As a result, today’s constellation of 24 US government-owned GPS satellites circle the globe, moving at 7000mph and an altitude of 12,600 miles, beaming out location and time data. Which brings us back to Heron the Greek and his mathematics.
|
Trilateration tells us where one point in space is (that’s us) from the intersection of hyperbolae* drawn from two other points in space (that’s the satellites), if their distance to the original point is known.
This means that your sat-nav receiver detects signals transmitted by up to nine of the GPS satellites (that’s how many are ‘visible’ at any one time). Each signal contains the time it was transmitted and the satellite’s position. Your sat-nav uses an internal clock to calculate the travel time for the signal, and thus the distance from itself to each satellite. Using trilateration, the receiver then knows exactly where it is in space relative to the satellites, and your position can be plotted on a pre-drawn map. Wonderful.
So the next time you casually punch some co-ordinates into your sat-nav, pause for a moment and consider Heron the Greek, some surprised Russian scientists, 269 dead South Koreans, and an American actor-turned-president. Because that’s what it took!
|