Constraining the Relative Inclinations of the Planets B and C of the Millisecond Pulsar PSR B1257+12

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 iB 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 less than or similar to M less than or similar to 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 less than or similar to i(B) less than or similar to 66 deg, with a corresponding relative inclination range 6 deg less than or similar to (i(C) - i(B)) less than or similar to 13 deg.