Section 5.5 · Home exercises · 4 of 4
Home exercise 5.5.4: How late is “now”?
How late is “now”?
#Electromagnetic signals travel at . Find
- the delay of a radio message from the Earth to the Moon (),
- the shortest and the longest time between sending a command to a rover on Mars and receiving its acknowledgement, if the distance varies between and ,
- the wavelength of a disturbance, and its phase lag at the end of a power line.
Every part is the delay , the time by which the retarded potentials lag behind their source. Part (c) turns the delay into a phase, .
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One way, at the closest and at the farthest. A command and its acknowledgement travel twice: to .
. The delay over is , which is of the period:
. The Mars range is the Mars–Sun distance plus or minus the Earth–Sun distance, roughly , which matches the to of the statement.
The line is long: an phase lag is noticeable, and long power lines are indeed analysed as transmission lines. A rover cannot be steered in real time: it receives a day's plan and drives on its own. The quasi-static approximation of circuit theory is the statement that the region is much smaller than , which is at .