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 65.0 days? (b) How much time does the pulsar take to rotate 6.00 × 106 times and (c) what is the associated uncertainty?

Explanation / Answer

(a) Here given data in ms. so that first we convert 65 day into ms.

ms in one day;

(24hr/1day) x (60min/1hr) x (60sec/1min) x (1000ms/1sec)

= 86,400,000 ms/day

ms in 65 day ;

65 x 86,400,000 = 5616000000 ms

rotation in 65 days N= (5616000000 ms)/(1.55780644887275 ms/rev)

= 3605069168.9 rev

= 3.60 x 109 rev

(b) Time the pulsar take to rotate 6.00 x 106 times = 6 x 106 x 1.55780644887275

= 9346838.693 ms

(c) Uncertainty in one rotation = 3 x 10-14 ms

multiply 1 x 106 by 3 x 10-14  = 3 x 10-8 ms

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