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Know Your Physics

Dr Lee Bridgeman
22 November 2017

Satellite

During the test of the first atomic bomb at Alamogordo, New Mexico, eminent physicist Richard Feynman was the only observer to view the explosion with the naked-eye. Feynman was concerned that by wearing the issued dark glasses he wouldn’t see anything, as the explosion was going to be 20 miles away. He concluded that, in this instance, the bright light wouldn’t be the problem, but ultraviolet light would be.  However, at this frequency, the ultraviolet light would readily be absorbed by glass; this realisation resulted in Feynman watching the whole event behind the windshield of a truck.  

Feynman was known as a great orator and was renowned for his profound statements. He is famously quoted saying:

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."  

Therefore, consider Einstein and his theories of special and general relativity, the latter suggesting that space-time is warped by a large gravitation field, which in turn, deviates light to follow the same geodesic path. This was confirmed experimentally by Sir Arthur Eddington and his team in 1919, when the known positions of stars deviated around the edge of the sun during a total eclipse. At the time, the accuracy of the data was questioned and said to be tainted by political motives after the First World War. However, the evidence stood, and Einstein became the first superstar physicist on the planet.

If we regress slightly, in 1714 the British government laid the gauntlet down to solve the major navigational problem of longitude.  Nautical navigation in principle requires a set of known values to create a positional fix at sea. When close to land, these are easy to find but at deep sea, landmarks disappear and this becomes a problem in determining where you are. The North to South lines of latitude were easily calculated by using the declination of celestial bodies, but to reach a destination it was critical to hold the course. This meant that the “over used” trade routes were known to all seamen, and piracy was prevalent. Eventually, legitimate solutions were presented and the challenge was initially solved by Galileo. He used the predictable orbits of Jupiter’s moons as an astronomical clock; unfortunately for him, his methods were found to be impractical on the deck of a rolling ship.

The riddle was finally solved by the genius engineer John Harrison, and his remarkable Marine Chronometer. The principle was simple and was based on two factors: the time at one’s home port and the position of the Sun at midday. As a vessel moved away from the home port the position of the Sun at midday changes, hence by angular calculation, a distance from east to west along the globe was calculated. Combining the line of longitude with the line of latitude gave a crosshair on a global chart and an estimated positional fix.  The science of navigation had taken huge step forward and created the key meridian line of longitude that runs through Greenwich to this day, and is a point from which all global time-zones are measured.

The next great step in navigation, was implemented by the US Department of Defence in 1973, with the deployment of the celestial Global Positioning System (GPS). This comprised 24 orbiting satellites at an altitude of 20,200 kilometres, travelling at a velocity of 3.9 kilometres per second in 6 orbital planes. Each satellite carried an extremely accurate on-board clock, which performed to dramatically improve global navigation potential across military, marine and aviation fields. GPS works by analysing radio-wave transmissions, sent by the orbiting satellites which provide a heavenly 3D coordinate, as well as a time every couple of micro-seconds. Using the early-day receivers, the global surface positional fix was then determined by using the known positions of three or more satellites in an array, and calculating their distance to the receiver. The distance was found by using the finite velocity of the speed of an electromagnetic wave.

Now here’s the issue, the satellites are at altitude, and moving fast. They enter the relativistic domain, which was proposed to affect space-time and ultimately, special relativity states that moving clocks run slow, and general relativity states that clocks in a weaker gravitational field run fast. In fact, before the launch of the satellite constellation, the onboard clocks were calibrated to take account of both anomalies, and as a result function to high accuracy in positional fixing. If they were not considered, then a global positional fix would simply not be achievable. In one nanosecond, an electromagnetic wave will travel 30cm, therefore in one day, an error of one nanosecond will produce a compunded error of approximately 25km. As a result of this, it would be impossible to get any positional fix. 

Time has played an enormous role in the advancement of navigational techniques. A simple fact to consider is that ultimate proof of Einstein’s Theory is realised every time you switch on a GPS system, as you must solve the fundamental laws of special and general relativity to gain an accurate position. Considering the concept that one day driverless cars will be guided by hyperfine GPS systems, the idea of “taking time” to complete a journey takes on a whole new meaning.