Time Uncertainty: Pulsar Rotation & Atomic Clocks

[GingerBread27]

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 1.424 806 448 872 75 2 ms, where the trailing 2 indicates the uncertainty in the last decimal place (it does not mean 2 ms).
(a) How many times does the pulsar rotate in 21.0 days?
The answer is 1.27e9
(b) How much time does the pulsar take to rotate 1.0 x 10^6 times? (Give your answer to at least 4 decimal places.)
The answer is 1424.8064 seconds
(c) What is the associated uncertainty of this time?

For this problem I am unsure of how the uncertainty is calculated. I understand parts a and b but not C. Please help.

 

[humanino]

Why don't you use upper and lower possible values for the period, calculate the two corresponding answers and make the difference between them ?

 

[M98Ranger]

The uncertainty in time for a pulsar rotation is typically calculated by considering the uncertainty in the measured rotation period. In this case, the uncertainty is represented by the trailing 2 in the given rotation period of 1.424 806 448 872 75 2 ms. This means that the actual rotation period could be anywhere between 1.424 806 448 872 75 0 ms and 1.424 806 448 872 75 4 ms.

To calculate the associated uncertainty in time, we can use the formula:

uncertainty in time = uncertainty in rotation period * number of rotations

For part (c), the uncertainty in time would be:

uncertainty in time = (0.00000000000000002 ms) * (1.0 x 10^6 rotations)

Thus, the associated uncertainty in time would be 0.02 ms. This means that the actual time for 1.0 x 10^6 rotations could be anywhere between 1424.8062 seconds and 1424.8066 seconds.

It is worth noting that this uncertainty may be smaller or larger depending on the precision of the measurements and the stability of the pulsar rotation.