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What I've Learned
If it wasn't for Einstein, the voice in your car couldn't tell you where to go.
To give directions, your car's Global Positioning System (GPS) communicates with satellites high above the earth. (Perhaps you don't have a GPS in your car, but chances are, you have one in your cell phone).
Before we get to the satellites, let's figure out where you are the old-fashioned way, using a compass and a map.
You begin by looking for prominent land marks – things that will show up on your map. You see a large hill. To your right, a tall radio tower. Perfect.
You face the hill and aim your compass at it. Your compass reading is called an azimuth. What you want is not the azimuth to the hill, but rather the azimuth from the hill back to you.
This is easy to determine. If your azimuth is less than 180 degrees, add 180 degrees. If the azimuth is 180 degrees or more, subtract 180 degrees. This is called the back azimuth. It is the direction from the hill back to you. Find the hill on the map and draw a line from it using the back azimuth. You can't pinpoint where on that line you are standing. All you know is that you are somewhere on that line.
(Yes, all you experts out there, I know about declination, but this is not a course in land navigation. I'm keeping it simple to make a point.)
Face the radio tower and aim your compass. Find the back azimuth the same way as before. This will give the direction back to you from the tower.
Locate the tower on the map and draw a line using the back azimuth. Again, you know you are somewhere on that line, but where?
Ah ha! Your location is where the line from the tower intersects the line from the hill. You have triangulated your position.
With satellites, the concept is the same. You use your relationship to known objects to determine where you are. In this case, the known objects are satellites orbiting 12,600 miles above the earth, traveling 8,700 miles per hour, which makes it a little trickier. Also, they are not on the same plane as you – they are way up in the sky and you are down on earth – so simple triangulation won't work.
It takes four satellites, not two, to figure out your location. There are 24 GPS satellites orbiting the globe, so the chances of the GPS unit in your car or phone picking up signals from at least four is pretty good. Each satellite broadcasts its location and the time. They are synchronized so that each sends this information at the same moment. Your GPS receiver considers there to be an imaginary sphere around each satellite – a sphere, not a circle. Where the spheres from four satellites intersect is where you are.
Because each satellite is sending its information at the same moment, data from satellites closer to you will arrive sooner than data from ones further away. This time difference is taken into account by the receiver and used to double check where each satellite is, and hence, where you are.
What about Einstein? I'm glad you asked.
According to Einstein's General Theory of Relativity, time moves slower for objects near strong gravitational sources and faster for objects further away. We down on earth are deeper in the gravity well, being here on the surface of the planet. Our clocks move a little slower than do those on satellites, which are higher up, further away from the surface.
Precise timing is necessary for GPS to work, so each satellite has an atomic clock that can measure time to the nanosecond – that's a billionth of a second. The difference in time between an atomic clock on earth and one in a GPS satellite is small, but measurable: about 45,900 nanoseconds per day.
Einstein's Special Theory of Relativity says that when one object is moving faster than another, time for the fast object slows down.
The classic example that is given – of course, it's never been done, but it's still the classic example – concerns a year-long space flight. You shake hands with your twin, climb aboard a space craft, wave goodbye, and travel for a year at near the speed of light.
During the year you are traveling, time slows down – way, way down – for you because you are moving so fast. To you, however, it doesn't seen to have slowed at all. The year seems like a year. The second hand seems to travel around the clock's face at its usual rate. Twenty-four hours seems like twenty-four hours. You move about at your normal pace. Time seems normal. And for you, it is.
Back on earth, time is moving at a much faster rate. To your twin, a minute seems like a minute and a year, like a year. But compared to you in the space craft, time is whizzing by.
When you return from your trip, one year has passed for you, but 200 years have passed on earth. Your twin is long dead.
A GPS satellite travels at a mere 8,700 miles per hour – a tiny fraction of the speed of light – so the time difference isn't much, only about 7,200 nanoseconds a day.
So, here's what we've got. Time for a GPS satellite is 45,900 ns/day faster than surface time because of its distance from the planet, but 7,200 ns/day slower because of its speed. Which means that overall, a GPS Satellite runs a net of 38,700 nanoseconds a day faster.
A 1,000 nanosecond difference between earth and satellite time throws off finding your correct location by almost 1,000 feet. A 38,700 nanosecond difference would throw things off by about seven miles. Every day, an additional seven miles.
What to do?
Before GPS satellites are launched, their atomic clocks are adjusted to run 38,700 nanoseconds a day slow. This means a GPS atomic clock is out of sync with a regular atomic clock. But once a satellite is launched and achieves orbit, time speeds up a bit for it and its atomic clock ends up in sync with earth clocks. Sweet.
The fact that the Theory of Relativity must be factored in for GPS to work properly amounts to what?
Ta da! Proof of the Theory of Relativity. Good job, Albert Einstein. Good job.