tokens: low-mass particles for the v200R1 model. The upper, middle, and bottom panels are the projected position of the each particles for φ = 30°, 45°, and 60°, respectively. The blue and red arrows show the radial velocity direction, moving toward or away from us, respectively. The size of the arrows indicates the tangential velocity. However, the number of particles approaching or moving away from us is dependent on the projected angle, but the explosion is not at all isotropic in the x -axis, which is the axis of movement of the massive particle. But the morphology of the explosion is similar to the one observed in Orion BN/KL. It is important to note that the massive particle in the Orion BN/KL explosion should be a runaway massive star with a velocity of at least 150 km s −1 , but the dynamical interaction of the massive star with clumps with a total mass comparable to the star’s mass could substantially decrease the velocity of the star at the end of the interaction. However, it is not the goal of this work to study the dynamic interaction of low-mass particles. 5. Conclusion We presented analytical and numerical solutions of the dispersion of particles due to dynamical interaction with a single massive particle. We have considered that the particles gather into a cluster and that they have a negligible mass with respect to the massive particle. The dynamical interaction with the massive particle produces a quasi-isotropic ejection of the particles. Then, we carried out a set of numerical simulations of spherical distribution of massless particles ( N -body simulations) for verifying our analytical solutions and obtaining an observational result. We have obtained a very good agreement between the numerical and analytical results. The main conclusions are that: 1. The gravitational ejection mechanism is able to accelerate small clumps or cloudlets (i.e., low-mass gas fragments) to jetlike velocities and, therefore, it should be thoroughly explored in future work. 2. The terminal velocity v ∞ of each particle is function of its own impact parameter. 3. The maximum terminal velocity is given by the limit when the particle has an impact parameter equal to zero and it is twice the velocity of the massive particle (. The minimal terminal velocity is related to the cluster radius. 4. The ejection angle of each of the particles is linearly related to the terminal velocity, and therefore is related to the impact parameter. Compact distributions of particles that are dynamically disturbed by a massive particle, which passes through the center of the distribution, produce more collimated ejections than in the case of more scattered clusters. 5. The resulting dispersion has an explosive signature, such as: (a) a small-scale common origin, (b) an isotropic distribution, and (c) velocities proportional to the distance from the common origin. This is the result of a short time interaction, which could be the mechanism that produced the explosive outflows.
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