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Semi-analytical theory of motion for the PSR B1257+12 planetary system

2000; Cambridge University Press; Volume: 177; Linguagem: Inglês

10.1017/s0252921100059078

2059-9137

M. Konacki, Andrzej J. Maciejewski, Alex Wolszczan,

Pulsars and Gravitational Waves Research

A planetary system around the pulsar B1257+12 has three planets A, B and C with the orbital periods of 25, 66 and 98 days, respectively (Wolszczan 1994). Dynamical properties of the system have been thoroughly studied by Rasio et al . (1993) and Malhotra (1993). They demonstrated that the gravitational interactions between planets B and C are significant enough to be detected. In such case, the motion of the system is no longer Keplerian and it is necessary to use a more precise description of motion in order to model the data properly. In this paper we derive a semi-analytical theory of motion assuming that the relative inclination of the orbits is small. We perform numerical simulations to show that our theory sucessfully predicts times of arrival of pulsar pulses and allows a determination of orbital inclinations and hence the masses of planets B and C.