ring composed of asteroidal dust particles should be trapped in exterior MMRs with the Earth (Jackson and The three-dimensional orbital evolution of interplanetary dust particles in mean motion resonances (MMRs) with planets Zook 1989). That such a ring could be detected was shown is investigated in a restricted three-body system. Using the by Dermott et al. (1994) in the IRAS observations and time variation of the Jacobi ''constant'' due to drag forces, we confirmed by Reach et al. (1995) with the COBE observadevelop simple analytical expressions that describe the orbital tions. evolution of a dust grain in MMRs with a planet. Together Dust particles are also trapped in MMRs with other with the time rate of change of the Tisserand criterion, the planets, and form additional circumsolar dust rings. These variations in eccentricity and inclination of a dust grain in any include the asteroidal and Trojan dust particles trapped in MMR are related to each other in one single equation. When a 1 : 1 MMR with Jupiter (Liou and Zook 1995), Kuiper expanded to the second order in eccentricity and inclination, belt dust particles trapped in exterior MMRs with Neptune the equation can be split into two parts and be used to describe and Uranus (Liou et al. 1996), and Tempel-type cometary separately the time variation of both orbital elements of a dust grain in a MMR. Dust grains in retrograde orbits in MMRs are dust particles trapped in a 1 : 2 interior MMR with Jupiter also discussed. Numerical simulations of various Sun-planet-(Liou and Zook 1996). The effects of drag forces and dust three-body systems are performed to verify the new anatrapping in exterior MMRs with a planet, combined with lytical expressions. Simulations of different types of dust grains the observed exclusion of dust in an interior zone, were (asteroidal, cometary) in MMRs with planets in the real Solar used to predict the existence of a planet around Ν± Pictoris System are also discussed and compared with our analytical (e.g., Roques et al. 1994).
predictions.