Time standards are now based on atomic clocks. A promising second standard is ba

Question

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 1.55780644887275 ± 3 ms, where the trailing ±3 indicates the uncertainty in the last decimal place (it does not mean ±3 ms). (a) How many times does PSR 1937+21 rotate in 20.0 days? (b) How much time (in s) does the pulsar take to rotate 5.00 × 106 times and (c) what is the associated uncertainty, in s?

Explanation / Answer

(a.) Find out how many ms are in one day:
(24hr/1 day) x (60min/1hr) x (60s/1min) x (1000ms/1s)
= 86,400,000 ms/day
Divide that number by 1.557806... to get the number of rotations in one day. It equals about 5.5462 x 10^7. Multiply this by 20 to get the number of rotations in 20 days.

(b.)
Multiply 1.557806... by 10^6. You get about 1.55781 x 10^6. This is how many milliseconds it takes to rotate 10^6 times. Convert this number into seconds to get the final answer.

(c.) Uncertainty of one rotation: 3 x 10^-14 ms
Multiply (5.0 x 10^6) by (3 x 10^-14 ms). Then convert that answer into seconds.

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