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Chapter 8: GPS and a Real- T ime Situational Displa y 197

Figure 8.5 Three spheres intersecting.

by the ephemeris. This is one reason why it may take a while for a real GPS receiver
to establish a lock, as it must go through a considerable amount of data calculations to
determine actual satellite positions within its field of view.
In my example, the radii of the “location spheres” are determined by the receiver using
extremely precise timing signals contained in the satellite transmissions. Each satellite
contains an atomic clock to generate these clock signals. All satellite clocks are constantly
synchronized and updated from earth-based ground stations. These constant updates
are needed to maintain GPS accuracy, which would naturally degrade because of two
relativistic effects. The best way to describe the first effect is to retell the paradox of the
space-travelling twin.
Imagine a set of two twins, (male, female—doesn’t matter) one of whom is slated to take
a trip on a fast starship to our closest neighboring star, Alpha Centauri. This round trip will

Figure 8.6 Plane view of the three spheres intersecting.