Daily Physicist

Today is the birthday of Satyendra Nath Bose (1894-1974).
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Today’s Problem: Basic principle behind GPS

You have a clock that is exactly synchronized with a remote clock that is a distance \(D\) away. The remote clock has a radio transmitter that periodically transmits the current time. When you receive the transmitted signal, how can you determine the distance to the remote clock?

When you receive the transmitted time, compare it to the time on your clock then the distance you are from the transmitter will be given by

\[D=c\Delta t\] where

• \(c=\) speed of light in a vacuum \(= 2.998 \times 10^8\) m/s
• \(\Delta t=\) time difference between your clock and the remote clock

Example: If \(\Delta t=1.0\mu\)s then
\(D = (2.998 \times 10^8\) m/s\()(1.0 \times 10^{-6}\) s\() = 300\) m