Final answer:
In GPS, three theoretical position lines are required for a two-dimensional fix, as they allow the intersection of spheres to narrow down the position to two points, one of which is on Earth. Option C is correct.
Step-by-step explanation:
For a two-dimensional fix using GPS (Global Positioning System), a minimum of three theoretical position lines are required. This is because with one satellite, you know you are somewhere on a large sphere around that satellite. When a second satellite signal is acquired, the intersection of these two spheres narrows down your position to a circle.
The third satellite signal provides another sphere, and the intersection of these three surfaces reduces your possible locations to just two points. One of these points is usually not on Earth, so by process of elimination, you can find your position on the globe. Thus, the correct answer is c) 3.
GPS achieves its accuracy through synchronization of highly precise atomic clocks on the satellites, considering the fact that even a minute error in time measurement can lead to significant position discrepancies. Due to the speed of light, accurate time measurement to the nanosecond level is crucial for resolving positions to practical accuracies such as the 1.00 mm resolution you mentioned.