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

Question

5. 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 1.557 806 448 872 75 ± 3 ms, where the trailing ±3 indicates the uncertainty in the last decimal place (it does not mean ±3 ms). What is the associated relative error (uncertainty)?

Explanation / Answer

The number of rotations in 7 days N is given by:

N =(7 days)/(time per rotation). I will convert to seconds:

7 days = (7 days) ×86 400 s/da = 604 800 s

N = (6.048 × 105s)/(1.5578 × 103s/rev) = 3.88 × 108 rev. (3 sigdig because “7.00 days”)

Time for 106 rotations = (106)(1.557 806 448 872 75 × 103s) = 1557.806 448 872 75 s. Note the conversion from milliseconds to seconds.

The uncertainty is 3 in the last digit, or ±3 × 1011 s

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.