Casio fx-CG10 Advanced Operation Manual page 88

Fostering Advanced Algebraic Thinking with Casio Technology
Investigation 6.2—Long-Distance Radio Navigation
Did You Know?
GPS stands for Global Positioning System. It is made up of three parts; satellites
orbiting the Earth, monitoring stations on Earth, and the individual receivers
owned by consumers. GPS is used for disaster relief and emergency services, as
well as providing driving directions, accurate timing for things such as banking,
and even controlling power grids.
Reference: http://www.gps.gov/
The use of LORAN, long-distance radio navigation, was terminated by the U.S.
Coast Guard in 2010, as it was replaced by more modern GPS devices. However,
LORAN played an important role for more than 50 years, helping the Coast Guard
pinpoint ships and whales, among other objects, within a quarter mile. LORAN used
the concept of intersecting hyperbolas to work. Though our investigation concerns
navigation on the Earth, which is spherical in shape, we will simplify things by
conducting our work as if we are on a plane. The concepts are quite similar for a
sphere and the results would not be very different for the distances involved here.
A hyperbola is the set of points whose difference from two fixed points, called the
foci, is constant. Suppose a ship at sea was trying to determine its location. By
measuring the difference in time between two well-synchronized pulses coming
from stations hundreds of miles apart, the ship could calculate a hyperbola on which
its location must be. By repeating this process using pulses from two different
stations, a second hyperbola could be calculated. The intersection of these
hyperbolas allowed the ship to locate its position, assuming it knew its approximate
location (since intersecting hyperbolas can have more than a single point of
intersection).
Reference: www.navcen.uscg.gov