Why is math important to science
It is an objective and universal form of communication of science
Who built the GPS?
U.S. Department of Defense
HOw much did it cost to build GPS?
What is GPS?
a worldwide radio-navigation system formed from a constellation of 24 satellites and their ground stations.
How close in measurements can you get
better than a centimeter
How does GPS work? Step One:
The basis of GPS is triangulation from satellites
How does GPS work? Step Two:
To triangulate a GPS receiver measures distance using the travel time of radio signals
How does GPS work? Step Three:
To measure travel time, GPS needs very accurate timing which it achieves with some tricks.
How does GPS work? Step Four:
Along with distance, you need to know exactly where the satellites are in space. High orbits and careful monitoring are the secret.
How does GPS work? Step FIVE:
Finally you must correct for any delays the signal experiences as it travels thru the atmosphere.
How many satellites are needed to determine exact position
How is the distance to a satellite determined
By measuring how long a radio signal takes to reach us from that satellite
What has to be assumed to make measurements to the satellite?
Both satellite and receiver are generating same pseudo-random codes at exactly same time
how long psuedo-random code takes to reach us
travel time x speed of light = distance
Being off one thousandth of a second at the speed of light translates into how much error?
How can timing be made almost perfect?
HOw much do atomic clocks cost?
Every GPS receiver is what?
an atomic accuracy clock
Why don't receiver clocks have to be accurate?
Because an extra satellite range measurement can remove errors (the fourth satellite)
What is the GPS master plan?
The air force has injected each GPS satellite into a precise orbit with a 24th on reserve
HOw many satellites are in view at every point on the globe
Who and how are the GPS monitored?
By Department of Defense...they use very precise radar to check each satellite's exact altitude, position and speed
What are the errors
ephemeris errors - caused by gravitational pulls from moon and sun and by pressure of solar radiation on satellites and sent to satellites to be transmitted along with timing signals
What other errors occur
1.)As GPS signal passes thru charged particles of ionosphere and then thru water vapor in troposphere it gets slowed down a bit
2.)when signal bounces off various local obstructions before it gets to our receiver - multipath error
3.)intentional errors - in order to avoid terrorist groups using satellite as weapon - selective availablity
How do we minimize this error
1.)Predict what a typical delay might be on a typical day - modeling
2.)compare relative speeds of two different signals - dual frequency
Why did we discontinue SA?
To make GPS more responsive to civil and commercial users worldwide
Why do we need differential GPS?
Its a way to correct various inaccuracies in GPS system
How differential GPS works?
involves cooperation of two receivers, one stationary and one roving around making position measurements
Other ways to work with differential GPS?
2.) inverted DGPS - GPS receivers at location with transmitter GPS transmit position back to tracking office. Computer will do the calculations
Real-world applications of GPS
Mathematics the Language of Science