Hi! Today I will tell you about a recent study made in Serbia on the dynamical influence of the small planets Ceres and Vesta on the Asteroid Belt. This study, Secular resonances with Ceres and Vesta by G. Tsirvoulis and B. Novaković, has been accepted for publication in Icarus.

The Asteroid Main Belt

There are many small bodies in the Solar System, here we just focus on the so-called Main Belt, i.e. a zone “full” of asteroids, which lies between the orbits of Mars and Jupiter. The word “full” should be taken with care, since there are many asteroids populating it, but if we cross it, we would be very unlikely to meet one. This zone is essentially void. It is estimated that the total mass of these asteroids is only 4% of the mass of the Moon.

It is called “Main Belt” since the first asteroids were discovered in this zone, and it was long thought that most of them were in this Main Belt. At this time, hundreds of thousands of them have been identified, but the Kuiper Belt, which lies behind the orbit of Neptune, might be even more populated.

The dynamics of these bodies is very interesting. It could contain clues on the early ages of the Solar System. Moreover, they are perturbed by the planets of the Solar System, especially the giant planets.

As a consequence, they have pretty complex dynamics. Their orbits can be approximated with ellipses, but these are not constant ellipses. They are precessing, i.e. their pericentres and nodes are moving, but their semi-major axes, eccentricities and inclinations are time-dependent as well. To represent their dynamics, so-called proper elements are used, which are kind of mean values of these orbital elements, and which are properties of these bodies.

Ceres and Vesta

Ceres and Vesta, or more precisely 1 Ceres and 4 Vesta, are the two largest objects of the Main Belt, with mean radii of 476 and 263 km, respectively. So large objects could present complex interior structures, this is one motivation for the US space mission Dawn, which has orbited Vesta between July 2011 and September 2012, and is currently in orbit around Ceres, since March 2015.

This space mission has given, and is still giving, us invaluable data on these two bodies, like a cartography of the craters of Vesta, and the recent proof that Ceres is differentiated, from the analysis of its gravity field.

The orbital resonances

The asteroids are so small bodies than they are subjected to the gravitational influence of the planets, in particular Jupiter. The most interesting dynamical effect is the orbital resonances, which occur when a proper frequency of the orbit of the asteroid (for instance its orbital frequency, or the frequency of precession of its orbital plane, known as nodal precession) is commensurate with a proper frequency of a planet. In such a case, orbital parameters are excited. In particular, an excitation of the eccentricity results in a destabilization of the orbit, since the asteroid is more likely to collide with another body, and/or to be finally ejected from the Main Belt.

This results in gaps in the Main Belt. The most famous of them are the Kirkwood Gaps, which correspond to mean-motion resonances between the asteroids and Jupiter. When the orbital frequency of the asteroid is exactly three times the one of Jupiter, i.e. when its orbital period is exactly one third of the one of Jupiter, then the asteroid is at the 3:1 resonance, its eccentricity is excited, and its orbit is less stable. We thus observe depletions of asteroids at the resonances 3:1, 5:2, 7:3, and 2:1.

Another type of resonance are the secular resonances, which involve the precession of the pericentres and / or of the node (precession of the orbital plane) of the asteroid. In such a case, this is a much slower phenomenon, since the periods involved are of the order of millions of years, while the orbital period of Jupiter is 11.86 years.

The asteroid families

An analysis of the dynamics (proper elements) and the physical properties of the asteroids shows that it is possible to classify them into families. The asteroids of these families are thought to originate from the same body, which has been destroyed by a collision. They are usually named among the largest of these bodies, for instance Vesta is also the name of a family.

This study

In this study, the authors investigate the dynamical influence of Vesta and Ceres on the Main Belt. They particularly focus on the secular resonances, in identifying four of them, i.e. resonances with the precessions of the pericentres and nodes of these two bodies.

For that, they perform numerical integrations of the motion of 20 test particles over 50 Myr, perturbed by the 4 giant planets, with and without Ceres and Vesta, and show significant influence of these bodies for some of the particles.

Finally, they show that some asteroid families do cross these resonances, like the Hoffmeister family.

Some links

• The study, Secular resonances with Ceres and Vesta by G. Tsirvoulis and B. Novakovic, accepted for publication in Icarus, and made freely available by the authors on arXiv (thanks to them for sharing)
• The web site of Georgios Tsirvoulis
• The web site of Bojan Novaković
• The mission DAWN