The origin of irregular satellites of giant planets:
Most satellites in the Solar system are irregular and have orbits with a retrograde motion, or large eccentricity, or high inclination. We study the origin of outer moons of Jupiter, Saturn and Neptune by numerical modeling [2-6]. Left figure (from ): The trajectories of planetesimals around the Jupiter calculated within the three-body problem. These trajectories intersect the planetocentric orbits that populated by small satellites or bodies. Number of considered intersection points of planetocentric orbits and heliocentric trajectories varied for different models from 1-2 thousand to 74 thousand. Intersection points are places of possible collisions between planetesimals and small satellites or particles. A collision probability is proportional to a surface density of a circumplanetary disk and a flux of planetesimals. From each point of intersection we calculate 5-9 trajectories of centers of mass for clouds of debris created by collisions of bodies with different mass ratio. The trajectories and fates of more than a million of clouds of debris were calculated. Right figure : the evolution of the surface density of initially prograde disk around the Saturn. The negative surface density means that a density of captured retrograde particles dominate over a surface density of prograde particles. The number of points of intersection in this model is 28.5 thousand. The total number of calculated trajectories of debris is 256.4 thousand.
The right figure shows that the retrograde satellite Phoebe placed in the area of fast accumulation of captured retrograde bodies and debris. Other area of similar retrograde accumulation has the radius in two times larger than orbit of the Phoebe. Based on our Saturn-2 model, we predicted in 1995 "that the outermost group of not yet discovered retrograde satellites with semimajor axes of the orbits in the range a = 24 - 31 · 106 km (with a = 25 - 26 · 106 km being the most probable value, corresponding to R = 0.018 in Fig.2) may exist near Saturn. By their sizes, orbital properties, and origin, they must be analogs of Jupiter's retrograde satellites - Pasiphae group" .
New Saturnian moons: observational confirmation of our theoretical prediction:
A paper appearing in the July 12, 2001 issue of Nature discusses the discovery of the 12 new Saturnian satellites. The satellites were discovered between August and December 2000 by an international team of observers.
The spatial distribution of new irregular satellites is very close to predicted distribution. According to our modeling (see right figure) outermost retrograde satellites of Saturn may have radii from 19 to 31 million km; observers discovered outermost group of 5 retrograde satellites with orbits 18.7-23.1 million km, where the larger satellite has the orbit 23.1 million km. Our simulation also shows areas of prograde satellites around orbit of retrograde Phoebe: in areas 7-12 and 15-19 million km. This prediction also agree with new discoveries of two prograde satellites near the orbit 11.4 million km and a group from 5 prograde satellites between 15.2-18.2 million km (also one small retrograde satellite was found inside this group on radius 15.6 million km, but prograde satellites clearly dominate in this area) (orbital parameters can be found here). It is a very strong evidence that the formation of irregular satellites is not really stochastic: they were captured into the most probable orbits.
In January 2002 we published additional prediction from our model 1994-1995: "From our modeling we expect a large group of small retrograde Neptunian satellites beyond the orbit of Triton (> 0.5·106 km, see figure from [4,5]). Nereid is probably the largest member of family of prograde satellites mixed with more numerous family of smaller retrograde satellites" . In January 13, 2003 large team of observers announced discovery of new irregular satellites of Neptune (see circular) using images obtained in Aug. 2002. From 5 new Neptunian satellites 3 are retrograde and 2 are prograde, they mixed in area 15.7-48.4 million km.
The origin of the Moon, the Charon and binary asteroids:
Our new model explains origin of the regular satellites of earth-like planets like the Moon, the Charon and binary asteroids  without single catastrophic events [1, 7]. Basic elements of new model:
1. Most Moon material was delivered from Earth mantle by many impacts of large (~1-100 km) asteroids. This explains "low-iron" composition of the Moon as in Hartmann-Davis single-impact model.
2. Initial low-mass prograde protosatellite disk was collected around the proto-Earth as near other planets.
3. Collisions of Earth debris with particles of prograde protosatellite disk is key factor for collection of debris on stable orbits. Easy to show that prograde Earth debris effectively joined to prograde protosatellite disk vs. retrograde debris that returned to Earth. Due to prograde Earth rotation volume of prograde debris is larger than retrograde debris volume.
4. Calculations of ballistic transfer of angular moment show that protosatellite ring must have the optimal radius that is close to average semi-major axis of debris orbits: Earth debris push away a smaller ring and decrease moment of larger ring.
5. Massive low-iron ring near Earth accreted to the Moon. At final stage, Earth debris bombarded new-born Moon, which shows well known dichotomy of crater populations.
Predictions from new multi-impacts model:
a. Most satellites of asteroids must have prograde and circular orbits that close to equator of central body (as in Moon-Earth and Charon-Pluto systems);
b. Asteroids with satellites must have faster rotation than single asteroids;
c. Most low rotate asteroids (or earth-like planets) do not have satellites (as Venus and Mercury);
d. For same other conditions, relative mass of satellites can be larger for smaller asteroids;
e. The dichotomy of craters must be typical for the Charon, the Pluto and large satellites of asteroids;
f. The Moon must have chemical, isotopic and geological signatures of many different impacts of asteroids to the Earth.
Analysis of known binary asteroids support predictions a,b,c,d .
1. Gorkavyi, N.N. The New Model of the Origin of the Moon. 35th Meeting of the AAS Division on Dynamical Astronomy, April 2004, Bulletin of the American Astronomical Society, 2004, 36, N2. Available here.
2. Gorkavyi, N.N. & Taidakova, T.A. Discovered Saturnian and undiscovered Neptunian retrograde satellites. AAS 199th meeting, January 2002, Bulletin of the AAS, 2002, 33, N4. Available here.
3. Prokof'eva V.V., Taraschuk V.P. and Gorkavyi N.N. Satellites of asteroids. Physics - Uspechi. 1995, 38 (6), p. 623-649.
4. Gorkavyi, N.N. and Taidakova, T.A. The Model for Formation of Jupiter, Saturn and Neptune Satellite Systems. Astronomy Letters., 1995, v. 21 (6). p.939-945.
5. Gorkavyi N.N. and Taidakova T.A. Origin of the Triton. In Vernadsky-Brown Microsymp. 20, The Int.Work. Meeting on Comparative Planetology. M.: GEOHI, 1994. p. 25-26.
6. Gorkavyi N.N. Formation of satellite systems: prograde and retrograde satellites of Jupiter and Saturn. Astronomy Lett. 1993. v.19(6). p.448-456.
7. Gaftonyuk, N., Gorkavyi, N. The Origin and Rotation of Binary Asteroids, In: Dynamics and Physics of the Solar System Bodies, Kiev, 2004, in press. Available here.