The period derivative is the rate at which an object’s orbital or rotation period * P* is changing – ie the instaneous change in period divided by the change in time. In calculus terms this is simply

Sometimes physicists use the simple dot above a quantity to represent the derivative with respect to time * t*, so the period derivative

here the subscripts 0 and f refer to the initial and final conditions respectively.

**Applications**

- In pulsar astronomy the period derivative can be used to estimate a pulsar’s characteristic age and magnetic field strength.

- The ratio of a binary’s orbital period to orbital period derivative
gives a characteristic timescale upon which it is evolving.**P/(dP/dt)**

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