Tag Archives: Vesta

Asteroids: Main Belt

Rotational stability of Ceres and Vesta

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Hi there! The question we address today is: how stable are the rotations of Ceres and Vesta? Do you remember these two guys? These are the largest two asteroids in the Main Belt, and the spacecraft Dawn visited them recently. It gave us invaluable information, like the maps of these bodies, their shapes, their gravity fields, their rotational states…
The study I present you today, Long-term orbital and rotational motions of Ceres and Vesta, by T. Vaillant, J. Laskar, N. Rambaux, and M. Gastineau, wonders how permanent the observed rotational state is. This French study has recently been accepted for publication by Astronomy & Astrophysics.

Outline

Ceres and Vesta
Simulating their rotation
The rotational stability
A symplectic integrator for a long-term study
Diffusion of the fundamental frequencies
Obliquity variations up to 20 degrees
The study and its authors

Ceres and Vesta

I already told you about these two bodies. (1)Ceres (“(1)” because it was the first asteroid to be discovered) is known since January 1801. It has been discovered by the Italian astronomer Giuseppe Piazzi at Palermo Astronomical Observatory. The spacecraft Dawn orbits it since April 2015, but is now inoperative since November 1st, 2018. We see Ceres as a body with a rocky core and an icy mantle, possibly with an internal ocean.

Before visiting Ceres, Dawn orbited Vesta, between July 2011 and September 2012. (4)Vesta has been discovered 6 years after Ceres, in 1807, by the German astronomer Heinrich Olbers. This is a differentiated body, probably made of a metallic core, a rocky mantle, and a crust. It has been heavily bombarded, showing in particular two large craters, Rheasilvia and Veneneia. Vesta is the source of the HED (Howardite Eucrite Diogenite) meteorites, which study is an invaluable source of information on Vesta (see here).

The surface of Vesta (detail). © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
The surface of Vesta (detail). © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA

You can find below some numbers regarding Ceres and Vesta.

(1) Ceres (4) Vesta
Discovery 1801 1807
Semimajor axis 2.77 AU 2.36 AU
Eccentricity 0.116 0.099
Inclination 9.65° 6.39°
Orbital period 4.604 yr 3.629 yr
Spin period 9.07 h 5.34 h
Obliquity 4.00° 27.47°
Shape (965.2 × 961.2 × 891.2) km (572.6 × 557.2 × 446.4) km
Density 2.08 g/cm3 3.47 g/cm3

As you can see, Vesta is the closest one. It is also the most elongated of these bodies, i.e. you definitely cannot consider it as spherical. Both have significant orbital eccentricities, which means significant variations of the distance to the Sun (this will be important, wait a little). You can also see that these are fast rotators, i.e. they spin in a few hours, while their revolution periods around the Sun are of the order of 4 years. By the way, Vesta rotates twice faster than Ceres. Such numbers are pretty classical for asteroids.
You can also notice that Vesta is denser than Ceres, which is consistent with a metallic core.
Finally, the obliquities. The obliquity is the angle between the angular momentum (somehow the rotation axis… this is not exactly the same, but not too far) and the normal to the Sun. In other words, a null obliquity means that the body rotates along its orbit. An obliquity of 90° means that the body rolls on its orbit. An obliquity of 180° means that the body rotates along its orbit… but its rotation is retrograde (while it is prograde with a null obliquity).
Here, you can see that the obliquity of Ceres is close to 0, while the one of Vesta is 27°, which is significant. It is actually close to the obliquity of the Earth, this induces yearly variations of the insolation, and the seasons. On bodies like Ceres and Vesta, the obliquity would affect the survival of ice in deep craters, i.e. if the obliquity and the size of the crater prevents the Sun to illuminate it, then it would survive as ice.
From these data, the authors simulated the rotational motion of Ceres and Vesta.

Simulating their rotation

Simulating the rotation consists in predicting the time variations of the angles, which represent the rotational state of the bodies. For that, you must start from the initial conditions (what is the current rotational state?), and the physical equations, which rule the rotational motion.
For rigid bodies, rotation is essentially ruled by gravity. The gravitational perturbation of the Sun (mostly) and the planets affects the rotation. You quantify this perturbation with the masses of the perturbers, and the distances between your bodies (Ceres and Vesta), and these perturbers. To make things simple, just take Ceres and the Sun. You know the Solar perturbation on Ceres from the mass of the Sun, and the orbit of Ceres around it. This is where the eccentricity intervenes. Once you have the perturbation, you also need to determine the response of Ceres, and you have it from its shape. Since Vesta is more triaxial than Ceres, then its sensitivity to a gravitational should be stronger. It mostly is, but you may have some resonances (see later), which would enhance the rotational response.

The rotational stability

The question of the rotational stability is: you know, the numbers I gave you on the rotation… how much would they vary over the ages? This is an interesting question, if you want to know the variations of temperature on the surface. Would the ice survive? Would the surface melt? Would that create an atmosphere? For how long? Etc.
For instance, the same team showed that the obliquity of the Earth is very stable, and we owe it to our Moon, which stabilized the rotation axis of the Earth. This is probably a condition for the habitability of a telluric planet.

Let us go back to Ceres and Vesta. The authors focused on the obliquity, not on the spin period. In fact, they considered that the body rotated so fast, that the spin period would not have any significant effect. This permitted them to average the equations over the spin period, and resulted in a rotational dynamics, which moves much slower. And this allows to simulate it over a much longer time span.

A symplectic integrator for a long-term study

A numerical integration of the equations of the rotational motion, even averaged over the fast angle (I mean, the rotation period), may suffer from numerical problems over time. If you propagate the dynamics over millions of years, then the resulting dynamics may diverge significantly from the real one, because of an accumulation of numerical errors all along the process of propagation.

For that, use symplectic integrators. These are numerical schemes, which preserve the global energy of the dynamics, if you have no dissipation of course. But there are many problems of planetary dynamics, which permit you to neglect the dissipation.

When you can neglect the dissipation, your system is conservative. In that case, you can use the mathematical properties of the Hamiltonian systems, which preserve the total energy. That way, your solution does not diverge.

But how to determine whether your dynamics is stable or not? There are many tools for that (Lyapunov exponents, alignment indexes…) Here, the authors determined the diffusion of the fundamental frequencies of the system.

Diffusion of the fundamental frequencies

Imagine you orbit around the Sun, at a given period… actually the period depends on your semimajor axis, so, if it remains constant, then the orbital period remains constant. If your orbit is also disturbed by another perturber, you will see periodic variations in your orbital elements, which correspond to the period of the perturber. Very well. So, analyzing the frequencies which are present in your motion should give you constant numbers…

But what happens if your bodies drift? Then your frequencies will drift as well. In detecting these variations, which result from the so-called diffusion of the fundamental frequencies of the system, you detect some chaos in the system. I took the example of the orbital dynamics, but the same works for the rotation. For instance, the orbital frequencies appear in the time evolution of the rotational variables, since the orbit affects the rotation. But you also have proper frequencies of the rotational motion, for instance the period at which the angular momentum precesses around the normale to the orbit, and this period may drift as well…

The diffusion of the fundamental frequencies is one indicator of the stability. The authors also checked the variations of the obliquity of Ceres and Vesta, along their trajectories. They simulated the motion over 40 Myr (million years), in considering different possible numbers for the interior, and different initial obliquities.

Let us see now the results.

Obliquity variations up to 20 degrees

If you consider different possibilities, i.e. we do not know how these bodies were 40 Myr ago, then we see that it is theoretically possible for them to have been highly influenced by a resonance. This means that one fundamental frequency of the rotation would have been commensurable with periodic contributions of the orbital motion, and this would have resulted in a high response of the obliquity. For the present trajectories, the author estimate that the obliquity of Ceres could have varied between 2 and 20° these last 20 Myr, and the obliquity of Vesta between 21 and 45°.

To be honest, this is only a part of a huge study, which also investigates the stability of the orbital motions of Ceres and Vesta. Actually, these bodies are on chaotic orbits. This does not mean that they will be ejected one day, but that their orbits becomes uncertain, or inaccurate, after some tens of Myr.

The study and its authors

  • You can find the study here. The authors made it also freely available on arXiv, many thanks to them for sharing! And now the authors
  • Unfortunately I did not find any webpage for the first author Timothée Vaillant. You can find here the one of Jacques Laskar, second author of the study,
  • and the IAU page of Mickaël Gastineau.

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

Asteroids: Main Belt

Predicting the chemical composition of (4)Vesta

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Hi there! Today I present you a study entitled Chlorine and hydrogen degassing in Vesta’s magma ocean, by Adam R. Sarafian, Timm John, Julia Roszjár and Martin J. Whitehouse. This study has recently been published in Earth and Planetary Science Letters. The goal here is, from the chemical analysis of meteorites which are supposed to come from Vesta, understand the evolution of its chemical evolution. In particular, how the degassing of its magma ocean impacts its chemical evolution.

(4)Vesta

I have presented the small planet (4)Vesta in that post. Basically, it is one of the largest Main-Belt asteroids, with a mean radius of some 500 km. The craters at its surface and the dynamical models of the early Solar System show that Vesta has been intensively bombarded. The largest of these impacts were energetic enough to melt Vesta and trigger its differentiation between a pretty dense core, a shallow magma ocean and a thin crust.

Despite having been visited by the spacecraft Dawn, the magma ocean has not been detected. Its presence is actually confirmed by the analyses of meteorites which fell on Earth.

The HED meteorites

Every day, about 6 tons of material hit the surface of the Earth, after having survived the atmospheric entry. Mineralogists split these meteorites into several groups. 5% of these meteorites are HEDs, for Howardite-Eucrite-Diogenites. These are achondritic basaltic meteorites, which are supposed to present similarities with Vesta. This hypothesis has been proposed in 1970 after comparison of the spectrum of Vesta and the one of these meteorites, and enforced since by the observations and theoretical works. So, it is now accepted that these meteorites come from Vesta or bodies similar to it, and studying them is a way to study the chemical composition of Vesta.
In this study, only the Eucrites will be addressed. They represent most of the HEDs, and contain 2 phosphates: the merrillite and the apatite. Moreover, they are systematically depleted in volatile elements, compared to carbonaceous chondrites and the Earth.

Chemical analysis

The authors have analyzed the chemical composition of 7 samples of eucrites, which were found on Earth. They present a variety of thermal alteration. Comparing them would be like watching a movie of the process of evolution of the material during the degassing in the magma ocean. The analyses were conducted on two sites: the Natural History Museum Vienna, in Austria, and the Woods Hole Oceanographic Institution (MA, USA). The involved technology is the scanning electron microscopy, which consists in obtaining images from the interaction of the sample with a focused bean of electrons, supplemented with an energy-dispersive X-ray spectrometer. This spectrometer gives the spectral signature of the interactions of the electrons with the rock sample, and so reveals the elements which constitute it.

The authors were particularly interested in measuring the concentrations of halogen (fluorine, chlorine, bromine and iodine), of stable isotopes of the chlorine, isotopes of hydrogen, and water. Comparing the relative concentration of these elements in the seven samples would give information on their volatilization during the outgassing process of the magma ocean, in conditions that do not exist on Earth.

Conclusions

The samples show different compositions in volatile elements (H2, H20, and metal chlorides), which show that there is some outgassing in Vesta’s magma ocean. The authors show in particular a large variability in the ratio [Cl]/[K], i.e. chlorite with respect to potassium. This means that not only the thermal evolution tends to reject volatile elements, but also that they are effectively ejected. This might be a concern since the ocean cannot be seen at the surface of Vesta. Anyway, this does not preclude outgassing, either through the crust, which is supposed to be thin, and/or with the assistance of giant impacts, which created craters deep enough to reach the ocean.

This way, we have a signature of the history of a planetary body in material found on the Earth. These results might have implications beyond Vesta, i.e. could be extended to other dwarf planets, and so give us information on the chemical evolution of the Solar System.

I hope you enjoyed this article. As usual, I am interested in your feed-back. So please, leave me some comments, share it, and happy new year!

To know more…

  • The study, which can also be found on ResearchGate, thanks to the authors for sharing!
  • The webpage of Adam Robert Sarafian, grad student at the Woods Hole Oceanographic Institution (USA)
  • The webpage of Timm John, Freie Universität Berlin, Germany
  • The webpage of Julia Roszjár, Natural History Museum, Vienna, Austria
  • The webpage of Martin Whitehouse, Swedish Museum of Natural History, Stockholm, Sweden
Asteroids: Main Belt

Interesting polar craters on Vesta

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Hi there! Today’s post is on the paper On the possibility of viscoelastic deformation of the large south polar craters and true polar wander on the asteroid Vesta, by Saman Karimi and Andrew J. Dombard, both at the University of Illinois at Chicago during the study; Saman Karimi is now at Johns Hopkins University. This study has recently been accepted for publication in Journal of Geophysical Research: Planets. It is a study of 2 craters of the small planet Vesta, Rheasilvia and Veneneia, which present two unusual features:

  1. they are located close to the South Pole,
  2. they are shallow with a central peak.

The authors have tried to explain these two properties.

The small planet Vesta

Vesta, or more precisely (4) Vesta, is the second largest object of the Main Asteroid Belt. It has a triaxial shape, i.e. (572.6 × 557.2 × 446.4) km, and is large enough to have a differentiated structure. It orbits at a distance of 2.36 AU from the Sun, i.e. 354 millions km, which implies an orbital period of 3.63 years. However, it rotates much more rapidly, in 5.3 hours. This rapid rotation is responsible for the high polar flattening, i.e. you can see from its shape that one of its axes is much smaller than the other ones. This axis is actually the rotation axis. This rotation around one axis permits to define easily the North and the South Poles, close to which are the 2 craters of interest.

(4) Vesta has been recently the target of the space mission Dawn. Dawn has been launched from Cape Canaveral in September 2007. It has orbited Vesta between July 2011 and September 2012, and is orbiting Ceres since March 2015. Dawn permitted invaluable progress on our knowledge of Vesta. It gave us an accurate cartography of the surface, which resulted in a count of the craters, measurements of its shape, of its gravity field, of its rotation… All of these data permit to constrain the interior. Many papers on Vesta followed, the paper I am presenting you is one of these.

Impacts in the Solar System

The Solar System bodies are impacted since the beginning of their formation. During the early ages of the Solar System, the impacts were more frequent than now, because of the presence of a protoplanetary disk composed of small objects before they accrete into larger ones. For instance, the Late Heavy Bombardment (LHB) is known as an episode of intense bombardment which occurred approximately 4 billion years ago. Some models consider that it could have been triggered by a gravitational interaction between giant planets and a former asteroid belt, which has destabilized it. For instance a previous version of the Nice model stated that the LHB could have been the consequence of a former 2:1 mean-motion resonance between Jupiter and Saturn during their migration. That resonance would have raised the orbital oscillations of these planets, which would have favored the destabilization of the asteroid belt and the bombardment of the terrestrial planets.

Meteorites are signatures of impacts on the Earth. Actually, many small objects are destroyed when they enter our atmosphere, this is why we get these small meteorites on the surface. Atmosphereless bodies usually present signatures of bombardment, for instance the Moon is known for its craters. When such a body does not present evidence of craters, it could mean that its surface has been recently renewed by some internal processes, due to tectonic or volcanic activity. So, counting the impacts is a way to age the surfaces.

When large enough, impacts can be responsible for dramatic events such as: the creation of the Moon, which has probably been split from the Earth by an impact, the creation of the rings of Saturn, which could be made of a large impactor, the destruction of the outer envelope of the proto-Mercury, or the extinction of the dinosaurs.

The study I present here deals with two impact basins at the South Pole of Vesta: Rheasilvia and Veneneia, with diameters of 505 and 395 km, respectively. You can compare these numbers with the dimensions of Vesta, and you understand how significant the impacts creating these craters should have been in the history of Vesta.

A viscoelastic rheology

The issue is: how does the surface respond to a large impact? It depends on its structure, of course. Basically, when you hit the surface, you create a crater, ejecta being expelled. After that, the surface of the asteroid tends to relax, i.e. the deformation due to the impact is kind of damped, but the final aspect will not be the initial one, since some material has been displaced, some other ejected, and the heating due to the impact tends to molten the surface. During the process of relaxation, the material tends to converge to the center of the basin, while it was pushed to the edges when the impact occurred, this can result in a central peak. Measuring the topography of the crater, i.e. its width, its depth, and the height of its central peak, can give constraints on the way the surface responds. This response characterizes the rheology of the surface, which is basically viscoelastic. Elastic would mean that the surface would recover its initial shape without any energy loss, and viscous means that you have actually some energy loss, which results in a permanent deformation once the surface is relaxed.

This study

The study first points out the two peculiarities of the two craters, and test the hypothesis that the impacts occurred close to the equator As a consequence Vesta would have been reoriented, this would explain why the impacts are now located close to the South Pole. This would mean that the surface is molten enough to result in the current topography of the craters and in the present polar flattening of Vesta.

To try to understand these facts, the authors assumed that the impactors hit Vesta close to its equator, and ran numerical simulations to check whether Vesta was able to reach its current state, which implies reshaping and reorientation. The numerical simulations consist to propagate the response to the impact not only in time, but also on the surface of Vesta. For that, the surface is discretized on a mesh, and finite elements modeling is used. This is a classical way to integrate Partial Derivative Equations (PDE). A key parameter is the temperature: if the impact is energetic enough, then Vesta heats enough to be molten enough to create the central peak, relax the crater, and reshape according to its new orientation state.

The reader should be aware that such simulations require high computation facilities, and take a long time. This is the reason why the authors ran only 8 of them, with different assumptions to cover most of the physically acceptable properties for the lithosphere of Vesta. These properties are in this study ruled by 6 parameters: the crustal thickness, the temperatures of the surface and of the mantle, the crustal thermal conductivity, the background heat flux, and the isostatic compensation. This last parameter characterizes the capacity of the surface to recover its gravity after the shock of the impact, which displaced the internal masses. This particularly affects the height of the central peak.

None of these 8 simulations result in a Vesta which is close enough to the observed one, since it does not heat enough. This means that the shape of Vesta is not a direct consequence of these two impacts, which probably occurred close to the South Pole, even if impacts at this latitude have a low probability.

A question for the authors

I am no specialist of impacts, but I wonder: if we have two tangent impacts instead of perpendicular ones, I guess they would have resulted in craters with a limited depth, but a strong reorientation of Vesta. The authors do not mention this possibility in the paper, and I would be interested in their opinion on this issue.

Some links

And please do not forget to comment! Thanks!

Asteroids: Main Belt

How Ceres and Vesta shape the asteroid belt

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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