Talk of the "International Workshop on Paolo Farinella (1953-2000): the Scientists, the man", Pisa, 14-16 June 2010

1. Asteroid shapes: From LASPA to
Current Ideas
Alberto Cellino, Carlo Comito, Paolo Tanga, Paolo Paolicchi,
Daniel Hestroffer, Derek Richardson, Aldo Dell’Oro

2. During the decade between 1980 and 1990, a
lot of work was done in asteroid science, and
the three guys below were very active

7. All this led to realize that Collisions have been a
major evolutionary process for the asteroid main belt
population

9. (ℓ is given in units of )

10. Available shape estimates do not fit very well... Because
asteroids are certainly not perfectly fluid bodies
Data from Poznan catalog, (maintained by A. Kryszczynska)

11. The basic idea
A gravitational aggregate will tend to minimize its Energy
E = Egrav + Erot
if it is not at equilibrium, it will evolve its shape and spin
in order to keep the Energy to the minimum possible
value, being given the total angular momentum of the
system.
The simple assumption is that, for a given Angular
Momentum, the overall rearrangement of the
configuration will be driven by the gradient of Energy.
We start from a variety of possible initial shapes, and
we look at how they evolve, for different values of A.M.

12. Using PKDGRAV (developed by D.C. Richardson)
Bodies are modeled as sets of equal-size, smooth (no surface
friction) spheres held together by gravity

13. 1.Start with a dispersed cloud of spherules,
and allow them to collapse to a spherical
assemblage under their own gravity.
2.Carve from this assemblage a set of
triaxial ellipsoids having different axial
ratios, each formed by about 1,000
spherules.
3.Apply a rigid rotation to reach a given
amount of (adimensional) Angular
Momentum, to characterize in this way a
set of different initial conditions.
4.Run PKDGRAV and follow the evolution of
each system.

25. Set of initial
shapes

37. The heritage of Paolo:
Gravitational aggregates
Stable quasi-equilibrium shapes, not identical to
theoretical equilibrium shapes for fluid bodies.
For increasing A.M., the flattening tends to increase.
Trend to reach b/a ≈ c/a in many cases
Compatible with friction angles (angles of repose) less
than 10°
Compatible with observed distribution of shapes of
relatively large asteroids.