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•• There are many subtle effects that must be taken into account in the GPS calculations. Here you are to estimate just the effect of the time dilation of special relativity. (a) Find the speed of a GPS satellite, using the height given in Fig. 2.12 and any other astronomical data (such as the earth’s radius) you need from Appendix A. Hence find the time difference between a clock in a satellite and one on the ground after one complete orbit, assuming they were initially synchronized. (Ignore all effects except time dilation.) (b) Supposing we forgot to allow for this time difference, estimate the resulting error in the calculation of our position.
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