Tag Archives: celestial mechanics

Asteroids: Near-Earth Objects

Thermal effects affect the rotation of asteroids

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Hi there! Today we discuss the rotation of asteroids. You know, these small bodies are funny. When you are a big body, you are just attracted by your siblings. The Sun, the planets, etc. But when you are a small body, your life may be much more chaotic! Such small bodies not only experience the influence of gravitational perturbations, but also of thermal effects, especially when they are close enough to the Sun (Near-Earth Objects). Not only you have radiation pressure of the Sun, due to the electromagnetic field, but also a torque due to the difference of temperature between different areas of the surface of the small body.
Investigating such effects is particularly tough, since it depends on the shape of the asteroid, which could be anything. Shape, surface rugosity, thermal inertia… and the rotation state as well. When you face the Sun, you heat, but with a delay… and meanwhile, you do not face the Sun anymore… you see the nightmare for planetary scientists? Well, actually, you can say that it is not a nightmare, but something fascinating instead. You bypass such difficulties by making simplified models, and if you have the opportunity to compare with real data, i.e. observations, then you have a chance to validate your theory.
Today I present Systematic structure and sinks in the YORP effect, by Oleksiy Golubov and Daniel J. Scheeres. This study, published in The Astronomical Journal, tells us that sometimes the thermal effects may stabilize the rotational state of the asteroids.

Outline

Yarkovsky and YORP
YORP cycles
Normal and tangential YORP
New equilibriums in the rotational state
Testing the prediction
The study and its authors

Yarkovsky and YORP

As I said, the most important of the thermal effects, which are experienced by small asteroids (up to some 50 km), is the Yarkovsky effect. The area which faces the Sun heats, and then reemits photons while cooling. The reemission of these photons pushes the asteroids in a direction, which depends on the rotation of the body. As a consequence, this makes the prograde asteroids (rotation in the same direction as the orbit) spiral outward, while the retrograde ones spiral inward. The consequence on the orbits is a secular drift of the semimajor axis, which has been measured in some cases.
The first measurement dates back to 2003. The small asteroid (530 m) 6489 Golevka drifted by 15 km since 1991, with respect to the orbital predictions, which considered only the gravitational perturbations of the surrounding objects.
This effect had been predicted around 1900 by the Polish civil engineer Ivan Osipovich Yarkovsky.

And now: YORP. YORP stands for Yarkovsky-O’Keefe-Radzievskii-Paddack, i.e. 4 scientists. This is the thermal effect on the rotation. Most of the asteroids have irregular shapes, i.e. they do not look like ellipsoids, but rather like… anything else. Which means that the reemission of photons would not average to 0 over a rotational (or spin) period. As a consequence, if the asteroid is like a windmill, then its rotation will accelerate. Rotational data on Near-Earth Asteroids smaller than 50 km show an excess of fast rotators, with respect to larger bodies. And theoretical studies have shown that YORP could ultimately destroy an asteroid, in making it spin so fast that it would become unstable. The outcome would then be a binary object.

This is anyway a very-long-term effect.

YORP cycles

In fact, when the rotational energy is not high enough to provoke the disruption of the asteroid, the theory of YORP predicts that the rotational states experience cycles, over several hundreds of thousands years. During these cycles, the asteroid switches from a tumbling state, i.e. rotation around 3 axes to the rotation around one single axis, and then goes back to the tumbling states. These are the YORP cycles, which are not really observed given their long duration. But the authors of this study tell us that these cycles may be disrupted.

Normal and tangential YORP

The authors recall us that the YORP effect, which generates these cycles, is in fact the normal YORP. There is a tangential YORP as well. This tangential YORP (TYORP) is due to heat transfer effects on the surface, which results in asymmetric light emission. This yields an additional force, which alters the rotation.

New equilibriums in the rotational state

And the consequence is this: when you add the TYORP in simulating the rotational dynamics of your asteroid, you get equilibriums, i.e. rotational state, which would remain constant with respect to the time. In other words, under some circumstances, the rotational state leaves the YORP cycles, to remain locked in a given state. These states would have a principal rotation axis, which would be either parallel to the orbit, or orthogonal. In this last case, the rotation could either be prograde or retrograde.

Testing the prediction

This study suggests that the authors have predicted a rotation state. It would be good to be able to test this prediction, i.e. observe this rotation state among the asteroids.
The study does not mention any observable evidence of this theory. As the authors honestly say, this is only a first taste of the complicated theory of the YORP effect. Additional features should be considered, and the mechanism of trapping into these equilibriums is not investigated… or not yet.

Anyway, this is an original study, a new step to the full understanding of the YORP effect.

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.

Asteroids: Trojans

The fate of Jupiter’s Trojans

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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.

Outline

The Trojan asteroids
These are dark bodies
Asymmetric populations
Numerical simulations
The Greek are more stable than the Trojans
Where are they now?
The study and its authors

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.

Asteroids: Centaurs, Asteroids: Main Belt, Asteroids: Trans-Neptunian Objects

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

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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.

Outline

Architecture of the Solar System
Planetary encounters
The Big Data approach
Random walk from one belt to another
The origin of Ceres
The origin of trapped satellites
The study and its authors

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.

Asteroids: Trans-Neptunian Objects

Weighing the Kuiper Belt

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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.

Outline

The Kuiper Belt
Planetary ephemerides
The Kuiper Belt as a ring
As many data as possible
Observed and fitted parameters
A light Kuiper Belt
The Planet Nine would have a limited influence
The study and its authors

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.

Zodiacal dust

Dust coorbital to Jupiter

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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.

Outline

The Trojan asteroids
Production of dust
Non-gravitational forces affect the dust
Numerical simulations
Some stay, some don’t…
Lucy is coming
The study and its authors

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.