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**Session 29 - Planets, Asteroids and Comets.**

*Oral session, Monday, June 08*

*De Anza/Mesa, *

## [29.03] Gravitational Scattering of Asteroidal and Cometary Particles on the Planets: Analytical Technique

*N. Gor'kavyi (Crimean Obs.), L. Ozernoy (CSI/GMU and GSFC/NASA), J. Mather (GSFC/NASA), T. Taidakova (Crimean Obs.)*
As we have demonstrated earlier (1997, ApJ 474, 496), the kinetic
equation written in the space of orbital coordinates such as semimajor
axis a and eccentricity e makes it possible to investigate
the gravitational scattering of particles on the planets in a fast
and effective way.
In the present work, we expand our previous 2-D analysis (inclination i=0)
to a much more general 3-D situation when i\not=0 and also include the
Poynting-Robertson drag (the latter is based on our method
described in 1997, ApJ 488, 268).
For a drifting particle (i.e. for its orbital torus), we compute a sample
of N gravitationally scattered particles flying by the planet at N
distances from the planet's center. The weight of each scattered particle
is proportional to the probability of the flyby within the ring whose
inner and outer radii are (r, r+dr), respectively. This enables us to
derive the scattering angle \phi as a function of r and the particle's
velocity V relative to the planet. Actually, for each (a,e,i)-particle
of velocity V, we find the distribution in r and therefore the
distribution in \phi. By evaluating the sum of such distribution for
all drifting particles produced by all available sources of dust, we get
the distribution in the net scattering angle. With the knowledge of
initial velocity components of particles, we compute the particle's
velocity components after scattering and therefore its new (a,e.i).

We illustrate this technique by computing the gravitational scattering
for dust particles of both asteroidal and cometary origin. The three main
results worth noting are: (i) the gravitational scattering leads to a much
thicker shape of the zodiacal cloud compared to the distribution
of the flat component of dust sources; (ii) large particles are scattered
more efficiently and therefore they would occupy a larger volume than the
smaller-size particles; and (iii) the drifting asteroidal dust is scattered
in a much more efficient way than the dust of cometary origin, which is
explained by smaller (on average) velocities of asteroidal particles.

**Program
listing for Monday**