Abstract
The three-dimensional orbital evolution of interplanetary dust particles in mean motion resonances (MMRs) with planets is investigated in a restricted three-body system. Using the time variation of the Jacobi “constant” due to drag forces, we develop simple analytical expressions that describe the orbital evolution of a dust grain in MMRs with a planet. Together with the time rate of change of the Tisserand criterion, the variations in eccentricity and inclination of a dust grain in any MMR are related to each other in one single equation. When expanded to the second order in eccentricity and inclination, the equation can be split into two parts and be used to describe separately the time variation of both orbital elements of a dust grain in a MMR. Dust grains in retrograde orbits in MMRs are also discussed. Numerical simulations of various Sun–planet–dust three-body systems are performed to verify the new analytical expressions. Simulations of different types of dust grains (asteroidal, cometary) in MMRs with planets in the real Solar System are also discussed and compared with our analytical predictions.
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