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 light-house 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). How many times does it rotate in 5.50 days?

Explanation / Answer

Divide 5.5 days by 1.55780644887275 ± 3 ms, but make sure to make the units match up first: 5.5 days = 5.5*24 hours = 5.5*24*60 minutes = 5.5*24*60*60 seconds = 5.5*24*60*60*1000 ms = 475200000 ms Number of rotations per 5.5 days is 475200000/1.55780644887275=305044314 Since you are manipulation a number with uncertainty by a number with no uncertainty, the uncertainty of this new answer is simply the original uncertainty divided by the 5.5, so: Number of rotations per 5.5 days is 305044314 ± 0.5455

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