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 dP/dt and is often expressed as a dimensionless quantity.

Sometimes physicists use the simple dot above a quantity to represent the derivative with respect to time t, so the period derivative dP/dt is often called P-dot, ie:

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 P/(dP/dt) gives a characteristic timescale upon which it is evolving.