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.

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:

• Dust arcs in the region of Jupiter’s Trojan asteroids,
• Comparison of the orbital properties of Jupiter Trojan asteroids and Trojan dust,
• and the homepage of Jürgen Schmidt.

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.