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. Suppose a pulsar rotates once every 1.615 731 448 872 75 ± 4 ms, where the trailing ± 4 indicates the uncertainty in the last decimal place (it does not mean ± 4 ms).

(a) How many times does the pulsar rotate in 30.0 days?


(b) How much time does the pulsar take to rotate exactly one million times? (Give your answer to at least 4 decimal places.)
s

(c) What is the associated uncertainty of this time?
±  s

Explanation / Answer

here,

time period for one rotation , T = 1.61573144887275 ms

T = 1.61573144887275* 10^-3 s

(a)

the given time , t = 30 days

t = 30 * 24 * 60 * 60

t = 259200 s

rotartion in 30 days, n = t/T

n = 259200 / (1.61573144887275* 10^-3)

n = 1.6 * 10^8 rotations

the pulsar rotates 1.6 * 10^8 rotations in 30.0 days

(b)

number of rotation , n = 1 million

n = 1000000

time taken for the pulsar take to rotate exactly one million times , t = n * T

t = 1000000 * 1.61573144887275* 10^-3

t = 1615.7314 s

time taken for the pulsar take to rotate exactly one million times is 1615.7314 s

(c)

associated uncertainty of this time = +- 4 *10^-14 * 10^6
ms

the associated uncertainty of this time is +- 4 *10^-8
ms

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