**DPS Pasadena Meeting 2000, 23-27 October 2000**

*Session 52. Solar System Origin I*

Oral, Chairs: R. Canup, D. Trilling, Friday, 2000/10/27, 10:30am-12:10pm, Little Theater (C107)
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## [52.10] AMD-stability and the Spacing of Planetary Systems

*J. Laskar (ASD/IMC-CNRS)*

I present here a simplified model of planetary accretion,
based on the conservation of mass, conservation of momentum,
and AMD-stability. I show how, within the limitations of
this model, the organization of generic planetary systems
can be derived from the knowledge of their initial mass
distribution. The angular Momentum Deficit (AMD) is the
difference between the angular momentum and the circular
angular momentum of the orbits : C = \sum_{k=1}^{n_p}
\Lambda_{k} (1-\sqrt{1-e_{k}^{2}}\cos i_{k}) . This quantity is
conserved in the secular system at all order, and bounds the
possible excursion of the eccentricities resulting from
planetary perturbations, even when the secular motion is
fully chaotic.

Let us assume that we have a distribution of planetesimals
of linear mass density \rho(a) =\zeta a^{p}. We assume that
the secular motion of these planetesimals is fully chaotic
and that they are only bounded by their AMD. Many collisions
wil occur, which we assume to be perfectly inelastic, with
conservation of the mass and of the momentum. As the mass of
the planetesimals increases, their excursion will be more
limited by the AMD constraint, until they cannot encounter
any longer any other particle.

It was possible to derive analytically the expression of the
final distributions resulting from this simplified accretion
model, for any initial mass distribution \rho(a) =\zeta
a^{p}. This derivation aggrees very well with the averaged
result of a numerical simulation of the same system.

For an initial constant linear mass distribution (p=0),
\sqrt{a} is proportional to the index of the planet n,
which is in very good agreement with our innner and outer
planetary system, and with the \upsilon-Andromedae
planetary systems.

Laskar, J: 2000, `On the Spacing of Planetary Systems', *
Phys. Rev. Letters*, **84**15, pp 3240--3243

The author(s) of this abstract have provided an email address
for comments about the abstract:
laskar@bdl.fr

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