Planetary and satellite three body mean motion resonances

•A method for calculating three body resonances between massive bodies is presented.•Dependence with masses, orbital elements and resonance order is showed.•Outwards and inwards migrations coexist inside a three body resonance.•An application to the Galilean satellites is presented. We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the orbital parameters and the order of the resonance and we compare with previous studies. We confirm that for low eccentricity low inclination orbits zero order resonances are the strongest ones; but for excited orbits higher order 3BRs become also dynamically relevant. By means of numerical integrations and the construction of dynamical maps we check some of the predictions of the method. We numerically explore the possibility of a planetary system to be trapped in a 3BR due to a migrating scenario. Our results suggest that capture in a chain of two body resonances is more probable than a capture in a pure 3BR. When a system is locked in a 3BR and one of the planets is forced to migrate the other two can react migrating in different directions. We exemplify studying the case of the Galilean satellites where we show the relevance of the different resonances acting on the three innermost satellites.