Orbital dynamics of PSR1257+12 and its two planetary companions

I present a review of the orbital dynamics of the three body problem of PSR1257+12 and its two putative planetary companions. The orbital dynamics provides two 'reality checks' on the planetary interpretation of the pulse arrival time residuals observed by Wolszczan and Frail (1992). First, by examining the dynamical stability of the system for the deduced orbital periods, one can place upper limits on the companion masses of about two times the mass of Jupiter. Since the lower limits of the companion masses deduced from the observations are well below this upper limit, the planetary interpretation passes this first 'reality check'. Second, the 3:2 near-commensurability of the orbital periods effects periodic variations of the Keplerian orbital parameters. The amplitude of these variations provides a direct measure of the masses of the companions relative to the mass of the pulsar. The signature of these variations in pulse time-of-arrival data is not straightforward, but, if the planetary interpretation is correct, it should become detectable as an additional quasi-periodic phase residual over a period of a few years.