Abstract
We investigate on the relative inclination of the planets B and C orbiting the pulsar PSR B1257+12. First, we show that the third Kepler’s law does represent an adequate model for the orbital periods P of the planets, because other Newtonian and Einsteinian corrections are orders of magnitude smaller than the accuracy in measuring P B/C. Then, on the basis of available timing data, we determine the ratio sin i C/ sin i B = 0.92±0.05 of the orbital inclinations i B and i C independently of the pulsar’s mass M. It turns out that coplanarity of the orbits of B and C would imply a violation of the equivalence principle. Adopting a pulsar mass range 1 ≲ M ≲ 3, in solar masses (supported by present-day theoretical and observational bounds for pulsar’s masses), both face-on and edge-on orbital configurations for the orbits of the two planets are ruled out; the acceptable inclinations for B span the range 36 deg ≲ i B ≲ 66 deg, with a corresponding relative inclination range 6 deg ≲ (i C − i B) ≲ 13 deg.
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Iorio, L. Constraining the relative inclinations of the planets B and C of the millisecond pulsar PSR B1257+12. J Astrophys Astron 31, 147–153 (2010). https://doi.org/10.1007/s12036-010-0015-8
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DOI: https://doi.org/10.1007/s12036-010-0015-8