Tag Archives: celestial mechanics

The fate of Jupiter’s Trojans

Hi there! Today we discuss about the Trojans of Jupiter. These are bodies which orbit on pretty the same orbit as Jupiter, i.e. at the same distance of the Sun, but 60° before or behind. These asteroids are located at the so-called Lagrange points L4 and L5, where the gravitational actions of the Sun and of Jupiter balance. As a consequence, these locations are pretty stable. I say “pretty” because, on the long term, i.e. millions of years, the bodies eventually leave this place. The study I present today, The dynamical evolution of escaped Jupiter Trojan asteroids, link to other minor body populations, by Romina P. Di Sisto, Ximena S. Ramos and Tabaré Gallardo, addresses the fate of these bodies once they have left the Lagrange points. This study made in Argentina and Uruguay has recently been published in Icarus.

The Trojan asteroids

Jupiter orbits the Sun at a distance of 5.2 AU (astronomical units), in 11.86 years. As the largest (and heaviest) planet in the Solar System, it is usually the main perturber. I mean, planetary objects orbit the Sun, they may be disturbed by other objects, and Jupiter is usually the first candidate for that.

As a result, it creates favored zones for the location of small bodies, in the sense that they are pretty stable. The Lagrange points L4 and L5 are among these zones, and they are indeed reservoirs of populations. At this time, the Minor Planet Center lists 7,039 Trojan asteroids, 4,600 of them at the L4 point (leading), and 2,439 at the L5 trailing point. These objects are named after characters of the Trojan War in the Iliad. L4 is populated by the Greeks, and L5 by the Trojans. There are actually two exceptions: (624) Hektor is in the Greek camp, and (617) Patroclus in the Trojan camp.

Location of the Lagrange points.
Location of the Lagrange points.

These are dark bodies

The best way to know the composition of a planetary body is to get there… which is very expensive and inconvenient for a wide survey. Actually a NASA space mission, Lucy, is scheduled to be launched in 2021 and will fly by the Greek asteroids (3548) Eurybates, (15094) Polymele, (11351) Leucus, and (21900) Orus in 2027 and 2028. So, at the leading Lagrange point L4. After that, it will reach the L5 point to explore the binary (617) Patroclus-Menetius in 2033. Very interesting, but not the most efficient strategy to have a global picture of the Trojan asteroids.

Fortunately, we can analyze the light reflected by these bodies. It consists in observing them from the Earth, and decompose the light following its different wavelengths. And it appears that they are pretty dark bodies, probably carbon-rich. Such compositions suggest that they have been formed in the outer Solar System.

Asymmetric populations

We currently know 4,600 Trojan asteroids at the L4 point, and 2,439 of them at the L5 one. This suggests a significant asymmetry between these two reservoirs. We must anyway be careful, since it could be an observational bias: if it is easier to observe something at the L4 point, then you discover more objects.

The current ratio between these two populations is 4,600/2,439 = 1.89, but correction from observational bias suggests a ratio of 1.4. Still an asymmetry.

Numerical simulations with EVORB

The authors investigated the fate of 2,972 of these Trojan asteroids, 1,975 L4 and 997 L5, in simulating their trajectories over 4.5 Gyr. I already told you about numerical integrations. They consist in constructing the trajectory of a planetary body from its initial conditions, i.e. where it is now, and the equations ruling its motion (here, the gravitational action of the surrounding body). The trajectory is then given at different times, which are separated by a time-step. If you want to know the location at a given time which is not one considered by the numerical integration, then you have to interpolate the trajectory, in using the closest times where your numerical scheme has computed it.

When you make such ambitious numerical integrations, you have to be very careful of the accuracy of your numerical scheme. Otherwise, you propagate and accumulate errors, which result in wrong predictions. For that, they used a dedicated integrator, named EVORB (I guess for something like ORBital EVolution), which switches between two schemes whether you have a close encounter or not.

As I say in previous articles like this one, a close encounter with a planet may dramatically alter the trajectory of a small body. And this is why it should be handled with care. Out of any close encounter, EVORB integrates the trajectory with a second-order leapfrog scheme. This is a symplectic one, i.e. optimized for preserving the whole energy of the system. This is critical in such a case, where no dissipative effect is considered. However, when a planet is encountered, the scheme uses a Bulirsch-Stoer one, which is much more accurate… but slower. Because you also have to combine efficiency with accuracy.

In all of these simulations, the authors considered the gravitational actions of the Sun and the planets from Venus to Neptune. Venus being the body with the smallest orbital period in this system, it rules the integration step. They authors fixed it to 7.3 days, which is 1/30 of the orbital period of Venus.

And these numerical simulations tell you the dynamical fate of these Trojans. Let us see the results!

The Greek are more stable than the Trojans

It appears that, when you are in the Greek camp (L4), you are less likely to escape than if you are in the Trojan one (L5). The rate of escape is 1.1 times greater at L5 than at L4. But, remember the asymmetry in the populations: L4 is much more populated than L5. The rates of escape combined with the overall populations make than there are more escapes from the Greek camp (18 per Myr) than from the Trojan one (14 per Myr).

Where are they now?

What do they become when they escape? They usually (90% of them) go in the outer Solar System, first they become Centaurs (asteroids inner to Neptune), and only fugitives from L4 may become Trans-Neptunian Objects. And then they become a small part of these populations, i.e. you cannot consider the Lagrange points of Jupiter to be reservoirs for the Centaurs and the TNOs. However, there are a little more important among the Jupiter-Family Comets and the Encke-type comets (in the inner Solar System). But once more, they cannot be considered as reservoirs for these populations. They just join them. And as pointed out a recent study, small bodies usually jumped from a dynamical family to another.

The study and its authors

You can find the study here. The authors made it freely available on arXiv, many thanks to them for sharing!

And now, the authors:

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.

The Solar System is a mess: Using Big Data to clear it up

Hi there! When you look at our Solar System, you wonder how it came to be that way. I mean, it formed from a nebula, in which grain accreted to create the Sun, the planets,… and all these small bodies. Most of them have disappeared since the origin, they were either ejected, or accreted on a planet, or on the Sun… anyway still many of them remain. You have the Asteroid Main Belt, the Centaurs, the Kuiper Belt, the Oort cloud, the comets… Several studies have tried to determine connections between them, i.e. where does this comet come from? Was it originally a Centaur, a Kuiper Belt Object, something else? And how did it change its orbit? A close approach with a giant planet, maybe?
And to address this question, you simulate the trajectories… which is not straightforward to do. It is pretty classical to simulate a trajectory from given initial conditions, but to answer such a question, you need more.
You need more because you do not know how reliable are your initial conditions. Your comet was there that day… very well. How sure are you of that? You observe a position and a velocity, fine, but you have uncertainties on your measurements, don’t you?
Yes, you have. So, you simulate the trajectories of many comets, which initial conditions are consistent with your observations. That’s better. And you hope that the outcome of the trajectories (trajectories simulated backward, if you want to know the origin) will be pretty much the same, since the initial conditions are very close to each other…
But they are not! This is what we call sensitivity to the initial conditions. This often means chaos, but I do not want to detail this specific notion. But basically, when a comet swings by a giant planet, its trajectory is dramatically deviated. And the deviation is highly sensitive to the location of the comet. So sensitive that at some point, you lose the information given by your initial conditions. C’est la vie.
As a result, there are in the literature many studies presenting their simulations, and which conclusions are sometimes inconsistent with each other.
The study we discuss today, It’s Complicated: A Big Data Approach to Exploring Planetesimal Evolution in the Presence of Jovian Planets, by Kevin R. Grazier, Julie C. Castillo-Rogez, and Jonathan Horner, suggests another approach to clear up this mess. It considers that all of these possible trajectories constitute a reservoir of Big Data. This study has recently been published in The Astronomical Journal.

Architecture of the Solar System

You know the 8 planets of our Solar System, from the closest to the outermost one:

  • Mercury,
  • Venus,
  • Earth,
  • Mars,
  • Jupiter,
  • Saturn,
  • Uranus,
  • Neptune.

And these planets are accompanied by many small bodies, which constitute

  • the Near-Earth Asteroids, which orbit among the 4 terrestrial planets (from Mercury to Mars),
  • the Main Belt Asteroids, which orbit between Mars and Jupiter,
  • the Centaurs, which orbit between Jupiter and Neptune,
  • the Kuiper Belt, which extends between 30 and 50 AU (astronomical units) from the Sun. So, its inner limit is the orbit of Neptune,
  • the scattered disc, which extends to 150 AU from the Sun. These objects are highly inclined. Eris is the largest known of them.
  • the detached objects, like Sedna. This population is very poorly known, and we do not even know if it is truly a population, or just some objects,
  • the hypothetical Oort cloud, which could be as far as one light-year, or 50,000 AU.

Of course, this list is not exhaustive. For instance, I did not mention the comets, which could originate from any of those populations of small objects.

In this study, the authors limit themselves to the orbit of Neptune. They consider 3 populations of objects between the orbits of Jupiter and Saturn, between Saturn and Uranus, and between Uranus and Neptune. And the question is: how do these populations evolve, to the current state? For that, planetary encounters appear to be of crucial importance.

Planetary encounters

Imagine a small body flying by Jupiter. It approaches Jupiter so closely that it enters its sphere of influence, in which the gravity of Jupter dominates the one of the Sun. Virtually, the object orbits Jupiter, but usually this orbit cannot be stable, since the approach is too fast. Locally, its orbit around Jupiter is hyperbolic, and the object does not stay there. Jupiter ejects it, and you do not know where, because the direction of the ejection is highly sensitive to the velocity of the object during its approach. It also depends on the mass of Jupiter, but this mass is very well known. Sometimes, the action of Jupiter is so strong that it fragments the object, as it did for the comet Shoemaker-Levy 9, in July 1994. And you can have this kind of phenomenon for any of the giant planets of the Solar System.

This is how planetary encounters could move, disperse, eject,… entire populations in the Solar System.

The Big Data approach

With so many objects (the authors considered 3 ensembles of 10,000 test particles, the ensembles being the 3 zones between two consecutive giant planets) and so many potential planetary encounters (the trajectories were simulated over 100 Myr), you generate a database of planetary encounters… how to deal with that? This is where the Big Data approach enters the game.

The authors performed it into two stages. The first one consisted to determine close encounter statistics and correlations, for instance with changes of semimajor axis, i.e. how a planetary encounter displaces an object in the Solar System. And the second stage aimed at reconstituting the path of the particles.

And now, the results.

Random walk from one belt to another

It appears that the particles could easily move from one belt to another. Eventually, they can be ejected. As the authors say, the classification of a particle into a population or another is ephemeral. It depends on when you observe it. In other words, a small object you observe in the Solar System could have been formed almost anywhere else. Even in situ. Now let us talk about specific examples.

The origin of Ceres

For instance, Ceres. You know, this is the largest of the Main Belt Asteroids, and the first to have been discovered, in 1801. It has recently been the target of the mission Dawn, which completed in October 2018.

Ceres seen by Dawn. © NASA
Ceres seen by Dawn. © NASA

Ceres is rich in volatiles like ammonia and carbon dioxides, as are other asteroids like Hygeia. Hygeia is itself a large Main Belt Asteroid. Knowing the origin of Ceres could give you the origin of these volatiles… but they could have been partly accreted after the migration… You see, it is difficult to be 100% sure.

Ceres could have formed in situ, i.e. between Mars and Jupiter, but this study shows that it could have originated from much further in the Solar System, and migrated inward.

The origin of trapped satellites

Most of the main satellites of the giant planets are thought to have been formed with the planet, in the protoplanetary nebula.
But in some cases, you have satellites, which orbit far from the parent planet, on an irregular orbit, i.e. a significantly inclined and eccentric one. In such a case, the body has probably not been formed in situ, but has been trapped by the planet. Among them are Saturn’s Phoebe and Neptune’s Triton, which are large satellite. I have discussed the case of Triton here. The trapping of Triton probably ejected mid-sized satellites of Neptune, which are now lost.

Phoebe seen by <i>Cassini</i> in August 2017 © NASA/ESA/JPL/SSI
Phoebe seen by Cassini in August 2017 © NASA/ESA/JPL/SSI
Mosaic of Triton taken by Voyager 2 in 1989. © NASA
Mosaic of Triton taken by Voyager 2 in 1989. © NASA

Phoebe and Triton entered the sphere of influence of their parent planet, but did not leave it. And where did they come from?

It seems probable that Triton was a Trans-Neptunian Object (TNO) before. In that part of the Solar System, the velocities are pretty low, which facilitate the captures. However, several scenarios are possible for Phoebe. The study show that it could have originated from an inner or from an outer orbit, and have jumped to Saturn from close encounters with Jupiter / Uranus / Neptune.

Something frustrating with such a study, which goes back to the origins, is that you lose some information. As a consequence, you can only conclude by “it is possible that”, but you cannot be certain. You have to admit it.

A way to secure some probabilities is to cross the dynamics with the physical properties, i.e. if you see that element on that body, and if that element is thought to have formed there, then you can infer something on the body, and the authors discuss these possibilities as well. But once more, you cannot be 100% sure. How do you know that this element has been formed there? Well, from the dynamics… which is chaotic… And when you see an element at the surface of a planetary body, does it mean that it is rich in it, or just coated by it, which means it could have accreted after the migration?

You see, you cannot be certain…

The study and its authors

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.

Weighing the Kuiper Belt

Hi there! Today, we are back to the Solar System, and more especially the Kuiper Belt. You know, all these small bodies, which orbit beyond Neptune. Instead of speaking of specific cases, like Pluto, Haumea or Sedna, we will see the Kuiper Belt as a whole.
The study I present, Mass of the Kuiper Belt, by E.V. Pitjeva and N.P. Pitjev, constrains its total mass with planetary ephemerides. This study has been recently published in Celestial Mechanics and Dynamical Astronomy.

The Kuiper Belt

I have presented the Kuiper Belt many times. These are objects, orbiting beyond the orbit of Neptune. This zone is named after the Dutch-American astronomer Gerard Kuiper, who hypothesized that it could have been a reservoir of comets, even if he thought that it would be almost clear. At that time, the only known Kepler Belt Object was Pluto. Now, more than 2,000 of them are known, and many more are probably to be discovered.
Most of these objects orbit between 30 and 50 AU (astronomical units) from the Sun.

This study wants to constrain the total mass of the Kuiper Belt, from the motion of the planets. For that, the authors built and used planetary ephemerides.

Planetary ephemerides

Planetary ephemerides give the location of the Solar System objects, especially the planets, at given dates. They have been of strategical importance during centuries for celestial navigation. Now, we still need them, for instance to identify potentially hazardous objects, to guide spacecraft, to detect new objects,…

I can cite 3 institutions, which provide ephemerides:

  • NASA’s JPL,
  • IMCCE, Paris Observatory, France,
  • Institute of Applied Astronomy, Russian Academy of Sciences.

JPL stands for Jet Propulsion Laboratory. It is located near Pasadena, CA, and is associated with the Californian Institute of Technology (CalTech). As part of NASA, it is associated with the American spacecraft.
The IMCCE, for Institute of Celestial Mechanics, is responsible for the French ephemerides. It has been founded in 1795 as the Bureau des Longitudes, in a context of rivalry between France and England. Its goal was then to assist France, to regain control of the seas.
And the Institute of Applied Astronomy, in Russia, is the place where this study has been conducted.

These 3 institutions provide their own ephemerides, i.e. solutions for the orbital motion of the planets, their satellites, the asteroids,… Now, let us see how to include the Kuiper Belt.

The Kuiper Belt as a ring

The orbital motion of planetary bodies come from the numerical integration of the gravitational equations, in which each body is perturbed by all the other ones… this makes many of them. So many that a common computer cannot handle that, when it comes to 2,000 of them. Moreover, there are probably many more Kuiper Belt Objects, which are not discovered yet, but which perturb the motion of the planets…

The authors by-passed this problem in modeling the Kuiper Belt as a ring. Not the whole Kuiper Belt actually. The 31 most massive of these objects are modeled as point masses, ans the remaining ones are embedded into a fictitious rotating ring, which mass perturbs the planets.

If you know the perturbation, you know the mass… Easy, isn’t it? Well, not that easy, actually…

As many data as possible

The authors maintain their ephemerides since many years, and each new version is enriched with new data. The current version, EPM2017, uses about 800,000 positional observations of planets and spacecraft, ranging from 1913 to 2015. Many of the observations of planets are Earth-based astrometric observations, while spacecraft observations include MESSENGER (mission to Mercury), Venus Express (to Venus), Cassini (to Saturn), and the Martian missions Viking-1 & 2, Pathfinder, Mars Global Surveyor, Odyssey, Mars Reconnaissance Orbiter, and Mars Express.

Very small objects like spacecraft are very sensitive to planetary perturbations, this is why their navigation data may be invaluable.

Observed and fitted parameters

Making ephemerides consists in fitting a dynamical model to data, i.e. observed positions. The dynamical model is mainly composed of the gravitational interactions between the planetary bodies, with some relativistic corrections (Einstein-Infeld-Hoffmann equations). These interactions use the masses of the objects as parameters.

When you want to fit the model to the data, you fit the initial conditions, i.e. the location of the objects at the beginning of the simulation, and some of the parameters. Why only some of them? It depends on how well you know them.

For instance, in this case, the mass of (1)Ceres is assumed to be accurately known, thanks to the Dawn mission (just finished, by the way). This means that fitting this mass would be counterproductive.

So, the authors have to make critical choices between what they fit and what they don’t, and also how they ponder the observations between each other.

A light Kuiper Belt

From formation models of the Solar System, the initial Kuiper Belt should be as massive as ten times our Earth. However,
fitting the ephemerides gives much smaller numbers. You can find below the outcomes of the previous studies and this last one, by the same team.

Year Kuiper Belt mass (in Earth mass)
2010 0.0258
2013 0.0263
2014 0.0197
2017 0.0228 ± 0.0046
2018 0.0197 ± 0.0035

As you can see

  • the current Kuiper Belt is by far much lighter than the original one. This means that this region of the Solar System has probably been depleted by the gravitational action of the main planets, only few objects remaining,
  • the numbers do not converge very fast, but they converge. In particular, each new measurement is consistent with the previous one, and the uncertainty tends to shrink. Slowly, but it shrinks.

This number of 0.02 Earth mass makes the Kuiper Belt about 2 orders of magnitudes (i.e. between 10 and 1,000) heavier than the Asteroid Main Belt, but some 3 orders of magnitude lighter than the proposed Planet Nine.

The Planet Nine would have a limited influence

You remember the Planet Nine? It is a yet undiscovered body, which is supposed to exist anyway. It should orbit far behind the orbit of Neptune, should be as massive as 10 Earth masses, and would be responsible for the clustering of the pericentres of the Trans-Neptunian Objects (the Kuiper Belt), and for the obliquity of the Sun.

In this study, the authors benefited from the very accurate navigation data of the space mission Cassini, which orbited Saturn until September 2017. And for Cassini, the Kuiper Belt has a much stronger influence than the hypothetical Planet Nine. This makes me think that the author believe that using such ephemerides is not a good strategy for constraining the Planet Nine.

Actually, the planetologists looking for the Planet Nine focus on the individual trajectories of the Kuiper Belt Objects, because these are the most sensitive to it.

The study and its authors

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.

Dust coorbital to Jupiter

Hi there! You may have heard of the coorbital satellites of Jupiter, or the Trojans, which share its orbit. Actually they are 60° ahead or behind it, which are equilibrium positions. Today we will see that dust is not that attached to these equilibrium. This is the opportunity to present you a study divided into two papers, Dust arcs in the region of Jupiter’s Trojan asteroids and Comparison of the orbital properties of Jupiter Trojan asteroids and Trojan dust, by Xiaodong Liu and Jürgen Schmidt. These two papers have recently been accepted for publication in Astronomy and Astrophysics.

The Trojan asteroids

Jupiter is the largest of the planets of the Solar System, it orbits the Sun in 11.86 years. On pretty the same orbit, asteroids precede and follow Jupiter, with a longitude difference of 60°. These are stable equilibrium, in which Jupiter and every asteroid are locked in a 1:1 mean-motion resonance. This means that they have the same orbital period. These two points, which are ahead and behind Jupiter on its orbit, are the Lagrange points L4 and L5. Why 4 and 5? Because three other equilibrium exist, of course. These other Lagrange points, i.e. L1, L2, and L3, are aligned with the Sun and Jupiter, and are unstable equilibrium. It is anyway possible to have orbits around them, and this is sometimes used in astrodynamics for positioning artificial satellites of the Earth, but this is beyond the scope of our study.

Location of the Lagrange points.
Location of the Lagrange points.

At present, 7,206 Trojan asteroids are list by the JPL Small Body Database, about two thirds orbiting in the L4 region. Surprisingly, no coorbital asteroid is known for Saturn, a few for Uranus, 18 for Neptune, and 8 for Mars. Some of these bodies are on unstable orbits.

Understanding the formation of these bodies is challenging, in particular explaining why Saturn has no coorbital asteroid. However, once an asteroid orbits at such a place, its motion is pretty well understood. But what about dust? This is what the authors investigated.

Production of dust

When a planetary body is hit, it produces ejecta, which size and dynamics depend on the impact, the target, and the impactor. The Solar System is the place for an intense micrometeorite bombardment, from which our atmosphere protects us. Anyway, all of the planetary bodies are impacted by micrometeorites, and the resulting ejecta are micrometeorites themselves. Their typical sizes are between 2 and 50 micrometers, this is why we can call them dust. More specifically, it is zodiacal dust, and we can sometimes see it from the Earth, as it reflects light. We call this light zodiacal light, and it can be confused with light pollution.

It is difficult to estimate the production of dust. The intensity of the micrometeorite bombardment can be estimated by spacecraft. For instance, the spacecraft Cassini around Saturn had on-board the instrument CDA, for Cosmic Dust Analyzer. This instrument not only measured the intensity of this bombardment around Saturn, but also the chemical composition of the micrometeorites.

Imagine you have the intensity of the bombardment (and we don’t have it in the L4 and L5 zones of Jupiter). This does not mean that you have the quantity of ejecta. This depends on a yield parameter, which has been studied in labs, and remains barely constrained. It should depend on the properties of the material and the impact velocity.

The small size of these particles make them sensitive to forces, which do not significantly affect the planetary bodies.

Non-gravitational forces affect the dust

Classical planetary bodies are affected (almost) only by gravitation. Their motion is due to the gravitational action of the Sun, this is why they orbit around it. On top of that, they are perturbed by the planets of the Solar System. The stability of the Lagrange points results of a balance between the gravitational actions of the Sun and of Jupiter.

This is not enough for dusty particles. They are also affected by

  • the Solar radiation pressure,
  • the Poynting-Robertson drag,
  • the Solar wind drag,
  • the magnetic Lorentz force.

The Solar radiation pressure is an exchange of momentum between our particle and the electromagnetic field of the Sun. It depends on the surface over mass ratio of the particle. The Poynting-Robertson drag is a loss of angular momentum due to the tangential radiation pressure. The Solar wind is a stream of charged particles released from the Sun’s corona, and the Lorentz force is the response to the interplanetary magnetic field.

You can see that some of these effects result in a loss of angular momentum, which means that the orbit of the particle would tend to spiral. Tend to does not mean that it will, maybe the gravitational action of Jupiter, in particular at the coorbital resonance, would compensate this effect… You need to simulate the motion of the particles to know the answer.

Numerical simulations

And this is what the authors did. They launched bunches of numerical simulations of dusty particles, initially located in the L4 region. They simulated the motion of 1,000 particles, which sizes ranged from 0.5 to 32 μm, over more than 15 kyr. And at the end of the simulations, they represented the statistics of the resulting orbital elements.

Some stay, some don’t…

This way, the authors have showed that, for each size of particles, the resulting distribution is bimodal. In other words: the initial cloud has a maximum of members close to the exact semimajor axis of Jupiter. And at the end of the simulation, the distribution has two peaks: one centered on the semimajor axis of Jupiter, and another one slightly smaller, which is a consequence of the non-gravitational forces. This shift depends on the size of the particles. As a consequence, you see this bimodal distribution for every cloud of particles of the same size, but it is visually replaced by a flat if you consider the final distribution of the whole cloud. Just because the location of the second peak depends on the size of the particles.

Moreover, dusty particles have a pericenter which is slightly closer to the one of Jupiter than the asteroids, this effect being once more sensitive to the size of the particles. However, the inclinations are barely affected by the size of the particles.

In addition to those particles, which remain in the coorbital resonance, some escape. Some eventually fall on Jupiter, some are trapped in higher-order resonances, and some even become coorbital to Saturn!

As a conclusion we could say that the cloud of Trojan asteroids is different from the cloud of Trojan dust.

All this results from numerical simulations. It would be interesting to compare with observations…

Lucy is coming

But there are no observations of dust at the Lagrange points… yet. NASA will launch the spacecraft Lucy in October 2021, which will explore Trojan asteroids at the L4 and L5 points. It will also help us to constrain the micrometeorite bombardment in these regions.

The study and its authors

You can find below the two studies:

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.

Some comets are not randomly distributed

Hi there! Everybody knows the comets, which may show us impressive tails, when they approach our Sun. This is due to what we call cometary activity. You can find comets in many places in the Solar System. Today we will focus on the 9 ones, which are located in the Main Asteroid Belt, i.e. between the orbits of Mars and Jupiter. This is the opportunity to present you Orbital alignment of Main-belt comets, by Yoonyoung Kim, Yougmin JeongAhn, and Henry H. Hsieh. This study has recently been published in The Astronomical Journal.

Comets in the Solar System

A comet is a small body, which presents some activity. This activity manifests as 2 tails, which are a gas tail and a dust tail. These two tails have different directions because the dust is heavier than the gas, and so is differently affected by the Sun. The Sun is actually responsible for at least part of this activity: if the body has water ice at its surface, the proximity of the Sun heats it enough to sublimate it.

We distinguish different classes of comets, from their orbital motion. The short-period comets have a period below 200 years, i.e. they make a close approach to the Sun periodically, with less than 200 years between two approaches. This is for instance the case of the famous Halley comet, or 1P/Halley, which period is 75 years. The comets with a period smaller than 20 years are called Jupiter-family comets, their orbits are strongly affected by the gravitational perturbation of Jupiter.
And we also have long-period comets, with periods larger than 200 years, up to several thousands of years, or even more… The extreme case is the one of the parabolic and hyperbolic comets, which eccentricities are close to or larger than 1. In such a case, we just see the comet once.

The Jupiter-family comets should originate from the Kuiper Belt, and have been so strongly perturbed by Jupiter that their semimajor axes became much smaller, reducing their orbital periods. However, we attribute the origin of the longer periods comets to the Oort cloud, which is thought to lie between 50,000 and 200,000 astronomical units (remember: the Sun-Earth distance is 1 AU). The comets we are interested in today are much closer, in the Main-Belt of asteroids.

The Main-Belt Comets

Main Belt Comets (MBCs) are comets, which are located in the asteroid belt. As such, they present some cometary activity. It appears that there is no general agreement on the way to identify them. Some asteroids present an activity, which is mainly driven by dust, and not by sublimation of water ice, so it could be relevant to call them active asteroids instead of comets. But they may have some sublimation driven activity as well.

The first identified MBC is 133P/Elst-Pizarro, which has been discovered in 1979 and is since then identified as an asteroid… and also as a comet since 1996. I mean, this is officially both a comet and an asteroid. The authors considered 9 MBC, there could be a little more of them, since classifying them is not that easy.

The comet Elst-Pizarro seen at La Silla Observatory. © ESO
The comet Elst-Pizarro seen at La Silla Observatory. © ESO

The MBC should originate from the Main-Belt. In this study, we are interested in the orbital dynamics. Let us talk about orbital elements.

Proper, forced, and osculating elements

As I have already told you in a previous post, we usually describe the orbit of a planetary body with 6 orbital elements, which characterize the ellipse drawn by the trajectory.

These orbital elements are

  • the semi-major axes (which would be the distance to the Sun, if the orbit were circular… this remains almost true for slightly eccentric orbits),
  • the mean longitude,
  • the eccentricity of the trajectory (0 means circular, the eccentricity must be smaller than 1 for the orbit to be elliptic),
  • the pericentre, i.e. location of the point of the trajectory, where the distance to the Sun is minimal,
  • the inclination, with respect to a given reference plane,
  • the ascending node, which locates the intersection between the reference plane and the orbit.

We call them osculating elements. These are the elements that the orbit would have at a given time, if it were exactly an ellipse. The real trajectory is very close to an ellipse, actually.

We will just keep in mind the two couples (eccentricity, pericentre), and (inclination, ascending node). Because these variables are coupled: without eccentricity, the pericentre is irrelevant, since the distance Sun-body is constant. And without inclination, the ascending node is irrelevant, since the whole trajectory is in the reference plane.

And these variables are the sums of a proper and a forced component. Imagine you are a MBC. You want to have your own motion around the Sun. This gives you the proper (or free) component, which is actually ruled by your initial conditions, and the interaction with the Sun (what we call the 2-body, or Kepler, problem). Unfortunately for you, there is this big guy perturbing your motion (Jupiter is his name). He is heavy enough to force your motion to follow his. This gives you a forced motion, and the actual motion is the sum of the proper and the forced ones. The forced motion tends to align your pericentre and your ascending node with the ones of Jupiter. The authors studied these motions.

The Main-Belt Comets are clustered

And their conclusions is that the MBC are clustered, in particular the pericentres. They tend to be aligned with the one of Jupiter. This could have been anticipated, but the authors found something more: the MBC are more clustered than the others asteroids, which lie in that region of the outer main-belt.

For quantifying this more clustered, they ran several statistical tests, which I do not want to detail (the Kolmogorov-Smirnov test, the F-test, and the Watson’s U2 test). These tests show that this excess of clustering happened very unlikely by chance. In other words, there is something. And this is more obvious for comets, for which the sublimation activity is overwhelming. This permits the authors to make a link between this activity, i.e. the presence of water ice, and this clustering. And to suggest favorable conditions for the detection of cometary activity for Main-Belt objects.

Where are the other MBCs?

Based on the result that the eccentricities of MBCs are secularly excited by Jupiter, the authors suggest to look for them in the fall night sky, when Jupiter’s perihelion is at opposition.
We would not necessarily be looking for new bodies, but also for cometary activity of already known bodies. Because of the variations of the distance with the Sun, the sublimation of water ice is not a permanent phenomenon. Remember that Elst-Pizarro has been classified as a comet 17 years after its discovery.

Clustering of TNOs suggests the existence of the Planet Nine

I would like to finish with a reminder that the Planet Nine was hinted that way, in 2016. A clustering among the orbits of Trans-Neptunian Objects was statistically proven. Since then, the Planet Nine has not been detected (yet), but other clues have suggested its presence, like the obliquity of the Sun.

More generally, I would say that big objects strongly affect the orbits of small ones, and in observing the small ones, then you can deduce something on the big ones!

The study and its authors

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.