On a Fokker-Planck approach to asteroidal transport
نویسندگان
چکیده
Recent studies show that chaotic motion should be considered as the rule rather than the exception in the asteroid belt, if the perturbations of many planets are taken into account. Assuming that asteroids are constantly diffusing away from the main belt, we may model their transport, i.e. the evolution of a distribution of initial conditions in the action space of the respective dynamical system, through a kinetic equation of the Fokker-Planck type. This consists in a two-step procedure: (i) calculation of the transport coefficients and (ii) solution of the diffusion equation, which depends critically upon the functional form of the transport coefficients. Recent results on this subject can be found in Varvoglis & Anastasiadis (1996) and Murray & Holman (1997) (hereafter M&H). The latter authors performed analytical estimates for the diffusion coefficients in mean motion resonances of the planar elliptic restricted three body problem (ERTBP). In this note, we present preliminary results on a numerical calculation of ‘local’ (action-dependent) diffusion coefficients. We selected for this study four mean motion resonances: the 5/3, 7/4, 9/5 and 12/7 resonances of the ERTBP. The ERTBP has a 2-D action space. However, diffusion through a mean motion resonance can be studied as a 1-D process, since resonant orbits may reach planet-crossing eccentricities while, at the same time, the semimajor axis remains practically unchanged. The actions are defined by L = p(1 )a and I = L(1 p1 e2) 12Le2, where a denotes the semimajor axis and e the eccentricity of the asteroid. The diffusion coefficient in the action I (similarly for L) is defined by D(I0) = lim t!1h( I)02i t = lim t!1h(I(t) I0)2i t (1)
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