Week 2: Vectors

In what other ways can we use vectors? Give one sample application and describe/illustrate how the vector can be used.

Many people use GPS (Global Positioning System) navigators, but not everyone knows that these devices constantly calculate vectors for you.

The Global Positioning System (GPS) is a satellite-based navigation system made up of at least 24 satellites. At most times and places, at least three satellites are visible. GPS satellites circle the Earth twice a day in a precise orbit. Each satellite transmits a unique signal and orbital parameters that allow GPS devices to decode and compute the precise location of the satellite. GPS receivers use this information and trilateration to calculate the user’s exact location. A calculation from three satellites will give the longitude and latitude of the receiver. A calculation from four satellites will also give altitude. Essentially, the GPS receiver measures the distance to each satellite by the amount of time it takes to receive a transmitted signal.

Now, how are vectors used in GPS? The receiver does not just triangulate its position once it constantly listens for the satellites and calculates changes in the receiver position from changes in the triangulation results, it also calculates any changes in distance and direction from the last known position. Within a very short time it has taken several readings, enough to calculate the velocity of your travel. The result? A speed in a particular direction – a velocity vector – which is always part of the receiver’s calculations.

Paul A. Tipler, Gene Mosca, Physics for Scientist and Engineers, p. 82