1. 13 April 20121 Navigation Alan Altschuler (Mr. A)

2. Why is Navigation Important? You need a path to get to your destination –That requires you to know where you are to start and updated locations while on the trip Sometimes, it is also important to just know where you are –So someone can send help –So someone can avoid you (another aircraft) –So you can build something if location is important Property ownership Political boundaries Precise measurements to align objects 2

3. How can you navigate? Sun –If away from the tropics, north/south at noon –Approximate east/west at sunrise/sunset Moon –Some insects use it Celestial –North Star (Polaris) –Southern Cross –Stars / Planets with charts –Eclipses with charts Inertial –With an original location –With acceleration Maps –With landmarks –With signs 3

4. How else can you navigate? These methods are particularly good when there are no landmarks Sun and a clock –Declination from zenith at noon (maximum height of sun) and a calendar provides latitude –Time offset between local noon and noon at a reference point gives relative longitude to reference point –Doesn’t work well near poles (either difficult or impossible to determine maximum height of sun). –Doesn’t work when sun is obscured by clouds. Global Positioning System (GPS) –Knowing distance from your location to multiple satellites (whose locations are known) provides your lattitude and longitude. –Doesn’t work when line-of-sight to satellites is obstructed –GPS was enabled by the space program, fast computers and the use of a universally invariant value (the speed of light). 4

5. 5 Each satellite orbits the earth twice a day. Their locations are always known. They are positioned in their orbits to provide coverage across the earth at any given time. The satellite continuously broadcasts a signal that includes its identification number and the time. A GPS receiver listens for satellites. –If it knows the time, it needs info from each of 3 satellites. 3 equations in 3 unknowns (lat, long, alt) –If it does not know the time, it needs info from each of 4 satellites. 4 equations in 4 unknowns (lat, long, alt, time) –However, the more satellites the better, in order to reduce the error. Inevitably, some the satellites will be near the horizon. As such, the error associated with altitude is the greatest. How does GPS work?

6. 6 Light travels a distance of 186,000 miles per second. If a computer can “listen” –1,000,000 times per second (1 megahertz), it can estimate the distance to a satellite within 0.186 miles (about 1,000 feet) –100,000,000 time per second (100 megahertz), it can estimate the distance to a satellite within 0.00186 miles (about 10 feet)

7. 7 If we are a certain distance from a satellite, we can say we are at one of a set of points The more accurate the clock, the better our prediction can be How does GPS work? Satellite Our possible location In blue ring Satellite Our possible location

8. 8 With 2 satellites, we can significantly make our prediction better How does GPS work? Satellites Our possible locations at intersections of rings

9. 9 With 3 satellites, we can make a much better prediction of where we are More satellites can reduce the error further How does GPS work? Satellites Our possible location

10. 10 Even more satellites Our possible locations