Accuracy of orbital period measurement
Let’s say you have measured the at times and , separated by N orbital cycles. Then the orbital period, , becomes:
From error propagation theory we know that if:
in which we are ignoring the partial derivative of with respect to because we consider to be zero. The equation becomes:
Then using (1) in (2):
In real life and are typically reported with uncertainties of the order d. Therefore, for a system with period h and , separated by one year we expect an uncertainty of d for the orbital period.