Halliday, Resnick & Walker — Measurement: Problem 16

16 Time standards are now based on atomic clocks. A promising second standard is based on pulsars, which are rotating neutron stars (highly compact stars consisting only of neutrons). Some rotate at a rate that is highly stable, sending out a radio beacon that sweeps briefly across Earth once with each rotation, like a lighthouse beacon. Pulsar PSR 1937+21 is an example; it rotates once every \(1.557\,806\,448\,872\,75 \pm 3 \text{ ms}\), where the trailing \(\pm 3\) indicates the uncertainty in the last decimal place (it does not mean \(\pm 3 \text{ ms}\)). (a) How many rotations does PSR 1937+21 make in \(8.00 \text{ days}\)? (b) How much time does the pulsar take to rotate exactly one million times and (c) what is the associated uncertainty?