The 24 satellites that orbit the earth and define the Global Positioning System use
precision atomic clocks that are accurate to 1 x 10-9 s, or 1 nanosecond (1ns). A person on the earth, using their mobile phone, can usually “see” 4-12 of the 24 satellites at any one time.
The satellites are moving, relative to the surface of the earth, at 1.4 x 104 km/h.
a- Calculate for one of these satellites,
Civilian GPS measurements have to be accurate at the level of 5-10m. How accurate must our knowledge of the clocks on the satellites be in order to achieve this level of accuracy in our position measurement?
[HINT: light signals are used by your phone and the satellites to perform the triangulation]
c-If we measure the passage of 1 day on earth using a clock that is identical to the clocks on the GPS satellites, how much time have the clocks on the satellites measured? What about for the passage of 2 days on earth? For this problem, it will be useful to apply the Binomial Expansion again