Monthly Archives: August 2018

Asteroids: Trans-Neptunian Objects

The rings of Haumea

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Hi there! I guess you have heard, last year, of the discovery of rings around the Trans-Neptunian Object Haumea. If not, don’t worry, I speak about it. Rings around planets are known since the discovery of Saturn (in fact a little later, since we needed to understand that these were rings), and now we know that there are rings around the 4 giant planets, and some small objects, which orbit beyond Saturn.

Once such a ring is discovered, we should wonder about its origin, its lifetime, its properties… This is the opportunity for me to present a Hungarian study, Dynamics of Haumea’s dust ring, by T. Kovács and Zs. Regály. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

Outline

The Trans-Neptunian Object (136108)Haumea
Rings beyond Jupiter
Numerical simulations
A gravitational and thermal physical model
A probable excess of small particles
The study and its authors

The Trans-Neptunian Object (136108)Haumea

Discovery

The discovery of (136108) Haumea was announced in July 2005 by a Spanish team, led by José Luis Ortiz, observing from Sierra Nevada Observatory (Spain). This discovery was made after analysis of observations taken in March 2003. As a consequence, this new object received the provisional name 2003 EL61.

But meanwhile, this object was observed since several months by the American team of Michael Brown, from Cerro Tololo Inter-American Observatory, in Chile, who also observed Eris. This led to a controversy. Eventually, the Minor Planet Center, which depends on the International Astronomical Union, credited Ortiz’s team for the discovery of the object, since they were the first to announce it. However its final name, Haumea, has been proposed by the American team, while usually the final name is chosen by the discoverer. Haumea is the goddess of fertility and childbirth in Hawaiian mythology. The Spanish team wished to name it Ataecina, after a popular goddess worshipped by the ancient inhabitants of the Iberian Peninsula.

Reanalysis of past observations revealed the presence of Haumea on photographic plates taken in 1955 at Palomar Observatory (we call that a precovery).

Properties

You can find below some numbers regarding Haumea.

Semi-major axis 43.218 AU
Eccentricity 0.191
Inclination 28.19°
Orbital period 284.12 yr
Spin period 3.92 h
Dimensions 2,322 × 1,704 × 1,138 km
Apparent magnitude 17.3

As a massive Trans-Neptunian Object, i.e. massive enough to have a pretty spherical shape, it is classified as an ice dwarf, or plutoid. This shape is pretty regular, but not that spherical actually. As you can see from its 3 diameters (here I give the most recent numbers), this is a triaxial object, with a pretty elongated shape… and this will be important for the study.

It orbits in the 7:12 mean-motion resonance with Neptune, i.e. it performs exactly 7 revolutions around the Sun while Neptune makes 12. This is a 5th order resonance, i.e. a pretty weak one, but which anyway permits some stability of the objects, which are trapped inside. This is why we can find some!

We can also see that it has a rapid rotation (less then 4 hours!). Moreover, it is pretty bright, with a geometrical albedo close to 0.8. This probably reveals water ice at its surface.

And Haumea has two satellites, and even rings!

Two satellites, and rings

Haumea has two known satellites, Namaka and Hi’iaka, named after two daughters of the goddess Haumea. They were discovered by the team of Michael Brown in 2005, simultaneously with its observations of Haumea, i.e. before the announcement of its discovery. You can find below some of their characteristics.

Namaka Hi’iaka
Semi-major axis 25657 km 49880 km
Eccentricity 0.25 0.05
Orbital period 18.28 d 49.46 d
Mean diameter 170 km 310 km
Keck image of Haumea and its moons. Hi'iaka is above Haumea (center), and Namaka is directly below. © Californian Institute of Technology
Keck image of Haumea and its moons. Hi’iaka is above Haumea (center), and Namaka is directly below. © Californian Institute of Technology

Usually such systems are expected to present spin-orbit resonances, e.g. like our Moon which rotates synchronously with the Earth. Another example is Pluto-Charon, which is doubly synchronous: Pluto and Charon have the same spin (rotational) period, which is also the orbital period of Charon around Pluto. Here, we see nothing alike. The rotational period of Haumea is 4 hours, while its satellites orbit much slower. We do not dispose of enough data to determine their rotation periods, maybe they are synchronous, i.e. with spin periods of 18.28 and 49.46 days, respectively… maybe they are not.

This synchronous state is reached after tidal dissipation slowed the rotation enough. Future measurements of the rotation of the two satellites could tell us something on the age of this ternary system.

And last year, an international team led by José Luis Ortiz (the same one) announced the discovery of a ring around Haumea.

Rings beyond Jupiter

In the Solar System, rings are known from the orbit of Jupiter, and beyond:

  • Jupiter has a system of faint rings,
  • should I introduce the rings of Saturn?
  • Uranus has faint rings, which were discovered in 1977,
  • the rings of Neptune were discovered in 1984, before being imaged by Voyager 2 in 1989. Interestingly, one of these rings, the Adams ring, contains arcs, i.e. zones in which the ring is denser. These arcs seem to be very stable, and this stability is not fully understood by now.
Arcs in the Adams ring (left to right: Fraternité, Égalité, Liberté), plus the Le Verrier ring on the inside. © NASA
Arcs in the Adams ring (left to right: Fraternité, Égalité, Liberté), plus the Le Verrier ring on the inside. © NASA

Surprisingly, we know since 2014 that small bodies beyond the orbit of Jupiter may have rings:

  • An international team detected rings around the Centaur Chariklo in 2014 (remember: a Centaur is a body, which orbits between the orbits of Jupiter and Neptune),
  • another team (with some overlaps with the previous one), discovered rings around Haumea in 2017,
  • observations in 2015 are consistent with ring material around the Centaur Chiron, but the results are not that conclusive.

These last discoveries were made thanks to stellar occultations: the object should occult a star, then several teams observe it from several locations. While the planetary object is too faint to be observed from Earth with classical telescopes, the stars can be observed. If at some point no light from the star is being recorded while the sky is clear, this means that it is occulted. And the spatial and temporal distributions of the recorded occultations give clues on the shape of the body, and even on the rings when present.

Why rings around dwarf planets?

Rings around giant planets orbit inside the Roche limit. Below this limit, a planetary object cannot accrete, because the intense gravitational field of the giant planet nearby would induce too much tidal stress, and prevent the accretion. But how can we understand rings around dwarf planets? Chiron presents some cometary activity, so the rings, if they exist, could be constituted of this ejected material. But understanding the behavior of dust around such a small object is challenging (partly because it is a new challenge).

In 2015, the American planetologist Matthew Hedman noticed that dense planetary rings had been only found between 8 and 20 AU, and proposed that the temperature of water ice in that area, which is close to 70 K (-203°C, -333°F), made it very weak and likely to produce rings. In other words, rings would be favored by the properties of the material. I find this explanation particularly interesting, since no ring system has been discovered in the Asteroid Main Belt. That paper was published before the discovery of rings around Haumea, which is far below the limit of 20 UA. I wonder how the Haumea case would affect these theoretical results.

In the specific case of Haumea, the ring has a width of 70 kilometers and a radius of about 2,287 kilometers, which makes it close to the 3:1 ground-track resonance, i.e. the particles constituting the ring make one revolution around Haumea, while Haumea makes 3 rotations.

Numerical simulations

Let us now focus of our study. The authors aimed at understanding the dynamics and stability of the discovered rings around Haumea. For that, they took different particles, initially on circular orbits around Haumea, at different distances, and propagated their motions.
Propagating their motions consists in using a numerical integrator, which simulates the motion in the future. There are powerful numerical tools which perform this task reliably and efficiently. These tools are classified following their algorithm and order. The order is the magnitude of the approximation, which is made at each timestep. A high order means a highly accurate simulation. Here, the authors used a fourth order Runge-Kutta scheme. It is not uncommon to see higher-order tools (orders between 8 and 15) in such studies. The motions are propagated over 1 to 1,000 years.

A gravitational and thermal physical model

The authors assumed the particles to be affected by

  • the gravitational field of Haumea, including its triaxiality. This is particularly critical to consider the ground-track resonances, while the actually observed ring is close to the 3:1 resonance,
  • the gravitational perturbation by the two small moons, Namaka and Hi’iaka,
  • the Solar radiation pressure.

This last force is not a gravitational, but a thermal one. It is due to an exchange of angular momentum between the particle, and the electromagnetic field, which is due to the Solar radiation. For a given particle size, the Solar radiation pressure has pretty the same magnitude for all of the particles, while the gravitational field of Haumea decreases with the distance. As a consequence, the furthest particles are the most sensitive to the radiation pressure. Moreover, this influence is inversely proportional to the grain size, i.e. small particles are more affected than the large ones.

And now, the results!

A probable excess of small particles

The numerical simulations show that the smaller the grains size, the narrower the final ring structure. The reason is that smaller particles will be ejected by the radiation pressure, unless they are close enough to Haumea, where its gravity field dominates.

And this is where you should compare the simulations with the observations. The observations tell you that the ring system of Haumea is narrow, this would be consistent with an excess of particles with grain size of approximately 1 μm.

So, such a study may constrain the composition of the rings, and may help us to understand its origin. Another explanation could be that there was originally no particle that far, but in that case you should explain why. Let us say that we have an argument for a ring essentially made of small particles.

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.

Moon

An Artificial Intelligence identifies the Lunar craters

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Hi there! Today we discuss about an algorithm. I guess you have already heard of Artificial Intelligence, and especially of some futuristic anticipations in which the world would be governed by robots… Fortunately, we are very far from that.

An Artificial Intelligence (AI), Google DeepMind’s AlphaGo, beat the Go professional player Lee Sedol in March 2016. Another AI, IBM’s DeepBlue, beat the then chess world champion Garry Kasparov in May 1997. These realizations of specific tasks belong to Narrow AI, while General AI would be Star Trek’s Data, i.e. a man-made system able to interact with its environments, and react better than a human would do.

Brent Spiner performing Data in Star Trek. © CBS Television Distribution
Brent Spiner performing Data in Star Trek. © CBS Television Distribution

In the context of planetary sciences, AI has recently permitted the discovery of exoplanets, from data analysis. The study I present today, Lunar crater identification via Deep Learning, by Ari Silburt et al., is another example of the way Artificial Intelligence may assist science. In this paper, the author challenge the computer to identify craters from images of the Moon and of Mercury, and the results appear to be very promising. This study has recently been accepted for publication in Icarus.

Outline

Craters in the Solar System
Artificial Intelligence, Machine Learning, and Deep Learning
Use of Digital Elevation Models of the Moon
Algorithm of crater identification
The relevant parameters
Success for the Moon
Successful transfer-learning to Mercury
The study and its authors

Craters in the Solar System

Let us forget AI for a short while. This is a blog of planetary sciences, remember? AI is a tool, not a goal. This study challenges a tool, which goal will be to identify craters. Hence, the goal is the craters.

Craters are ubiquitous in the Solar System, since it is intensively bombarded. This is especially true for the inner Solar System, since the impactors, i.e. small rocky bodies, are gravitationally attracted by the Sun. And while passing by, they may hit us, or the Moon, Mercury, Mars,… And we are lucky, since the current bombardment is much less intense than it was in the youth of the Solar System. Anyway, we have been intensively bombarded, we still are, but our atmosphere protects us in destroying the impactors, which reach the terrestrial surface as meteorites. A huge impactor is thought to be responsible for the extinctions of the dinosaurs, and may be one day… no, better not to think about it.

There are not so many craters at the surface of the Earth, partly because our atmosphere has eroded them, and partly because the geophysical activity relaxed them. But what about atmosphereless bodies like our Moon? Craters are everywhere!

And craters are the clock of the surface. If you see only craters, it means that the surface has not changed since the impact. The surface did not heat, did not melt, there was no geophysical activity creating failures, ridges,… For instance, in the satellites of Jupiter, you see almost no craters on Io and Europa, since there are active bodies. You see some on Ganymede, which is less active, and much more on Callisto, which is quieter.

The surfaces of the Galilean satellites of Jupiter Europa (left), Ganymede (middle), and Callisto (right), seen by Galileo. © NASA
The surfaces of the Galilean satellites of Jupiter Europa (left), Ganymede (middle), and Callisto (right), seen by Galileo. © NASA

This is why it is worthwhile to catalogue the craters of a given planetary body. But since it is a difficult and exhausting task, it is probably a good idea to tell a computer how to do it. This is where AI and Deep Learning come into play.

Artificial Intelligence, Machine Learning, and Deep Learning

As I told you, we are here interested in narrow AI: we want a computer to perform a specific task, and only that task, better than a human would do. And we want the computer to learn how to do it: this is Machine Learning. We give images of craters, tell the computer that they are craters, and we hope it to identify craters on images, which have not been studied yet, i.e. new data. Very well.

A common algorithm for that is Deep Learning. I do not want to go into specifics, but this uses several layers of neurons. Here, neurons should be understood as computing nodes performing a specific sub-tasks, and interacting with each others. The analogy with the human brain is obvious. In this specific case, the authors used convolutional neural networks, in which neurons layers are structured to perform a discrete convolution (a mathematical operation) between their inputs and a filter, which is represented by weights. These weights permit to ponder the relative roles of the different inputs of the system, i.e. which input is more relevant than another one…

The inputs are the planetary data.

Use of Digital Elevation Models of the Moon

Fortunately, we dispose of numerous topographic data of the Moon, which make it the ideal target for elaborating such an algorithm.

The authors used digital elevation maps (DEM) of the Moon, resulting from 2 different missions:

  1. the Lunar Reconnaissance Orbiter (LRO). This is an American mission, which orbits the Moon since 2009. It has made a 3-D map of the Moon’s surface at 100-meter resolution and 98.2% coverage, thanks to the Lunar Orbiter Laser Altimeter (LOLA), and the Lunar Reconnaissance Orbiter Camera (LROC).
  2. The Japanese mission SELENE (Selenological and Engineering Explorer), which is also known as Kaguya. It was composed of 3 spacecraft, i.e. a main orbiter and two satellites. It operated during 20 months, between September 2007 and June 2009. It was then intentionally crashed near the crater Gill.

The authors used such data to train the system, i.e. to make itself an expert in crater identification.

Algorithm of crater identification

Historically, the first identifications of craters were made by visually examining the images. Of course, this is an exhaustive task, and the human being has failures. Moreover, if a small crater looks like a circle, larger ones, i.e. with a diameter larger than 20 km, may have a central peak, may contain other craters, and/or may be altered by the topography (mountains…).

The consequence is that beside the time spent to perform this task, you would have false detections (you think this is a crater, but it is not), and miss some craters, especially the smallest ones. If someone else does the same task, from the same data, (s)he would get a significantly different list. Comparing these lists would be a way to estimate the identification errors.

So, you can see that the use of the numerical tool is inescapable. But how would you do that? Some algorithms identify the circles on the images thanks to a Hough transform (I do not want to go into specifics, but this is a mathematical transformation of your images which tells you “there is a circle there!”), some identify the edges of the craters, some do both… And Deep Learning is learning by itself how to identify craters.

This consists essentially of 3 steps:

  1. training,
  2. validation,
  3. tests.

The algorithm detects crater rims from their pixel intensities, then fits a circle on them, and give as outputs the coordinates of the center and the mean radius of the crater. The authors then compared the results with existing catalogues.

The relevant parameters

The detection of the craters uses parameters, for instance the threshold for the detection of variation of pixel intensities. And the efficiency of the algorithm is measured with

  1. the true positives Tp (the algorithm tells you there is a crater, and you know there is actually one),
  2. the false positives Fp (the algorithm tells you there is a crater, but there is none),
  3. the false negatives Fn (the algorithm tells you nothing, while you know there is a crater),

and these quantities are recombined as

  • the precision P = Tp/(Tp+Fp) (if the algorithm tells you there are 100 craters, how many are actually present?),
  • the recall R = Tp/(Tp+Fn) (over 100 craters, how many are detected by the algorithm?)
  • F1 = 2PR/(P+R), which permits to use a single-parameter metric.

    • The goal is of course to maximize F1.

    Beside this, the authors also compared the coordinates and radii of the detected craters with the ones present in the catalogues, i.e. which had been previously determined by other methods. And all of this works pretty well!

    Success for the Moon

    The algorithm detected 92% of the known craters. Moreover, it also announced to the authors the detection of 361 new craters, and showed to be particularly efficient for craters with a diameter smaller than 5 km. Not only these small craters are a challenge for the human eye, but their regular shape makes the automatic detection more reliable. So, you here have an example of a task, for which the computer could be more efficient than the human. Among these 361 new craters, the authors estimate 11% of them to be false positives (Fp). This last number has some uncertainty, since the validation of a crater is made by a human eye, and the outcome depends on the brain, i.e. the human, behind the eye.

    This is very promising but would that work on another body? It seems so…

    Successful transfer-learning to Mercury

    Finally, the authors asked the computer to identify craters on the surface of Mercury. Remember that the computer was trained with Lunar data. This is called a domain shift, and this is a challenge, since the surface of Mercury has not exactly the same properties of the Lunar one. The bombardment activity was different, Mercury was possibly partly resurfaced, the material itself is different…

    The Moon is on the left, and Mercury on the right.
    The Moon is on the left, and Mercury on the right.

    But the results are pretty good, i.e. many craters are actually detected.

    The algorithm needs some refinements. For instance, it may be lured by circular depressions, which are not true craters (false positives). But the results are very encouraging, in particular for identifying craters on bodies, for which no catalogue exists at this date. The last space missions have given Digital Elevation Models for Venus, Mars, Vesta, and Ceres, and this algorithm may prove very useful to identify their craters.

    Deep Learning is the future!

    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.

Comets

When a comet meets the Solar wind

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Hi there! Today, let us talk about the environment of a comet. As you know, a comet is an active body, which emits ionized particles and dust. The Sun itself emits charged particles, which constitute the Solar wind. We discuss today of the interaction between these two emissions. The environment of charged particles around a comet has been measured by the spacecraft Rosetta, and this has motivated modeling these interactions. I present you Solar wind dynamics around a comet: The paradigmatic inverse-square-law model, by M. Saillenfest, B. Tabone, and E. Behar. This study has recently been accepted for publication in Astronomy and Astrophysics.

Outline

The spacecraft Rosetta
The Solar wind
The physics of the interaction
Reducing the problem
An empty cavity around the comet
To come: comparison with in situ measurements
The study and its authors

The spacecraft Rosetta

Let us first speak about the mission Rosetta. Rosetta was a European mission, which orbited the comet 67P/Churyumov–Gerasimenko between 2014 and 2016. It was named after the Rosetta Stone, which permitted the decipherment of Egyptian hieroglyphs. The mission Rosetta was supposed to give us clues on the primordial Solar System, i.e. on our origins, from the study of a comet.

It was launched in March 2004 from Kourou (French Guiana), and then started a 10-years journey, during which it made 3 fly-bys of the Earth and one of Mars. You can say: “why going back to Earth?” The reason is that Rosetta was supposed to orbit 67P/Churyumov–Gerasimenko (spoiler alert: it did it). For this orbital insertion to be possible, it had to arrive slowly enough… but also had to leave Earth fast enough, to get rid off its attraction, and also to shorten the journey. Fly-bys permitted to slow the spacecraft in exchanging energy with the Earth (or Mars).

Rosetta also visited two asteroids: (2867) Šteins, and (21) Lutetia, in September 2008 and July 2010, respectively. It was inserted into orbit around 67P in August 2014, released the lander Philae in November, and the mission ended in September 2016. In particular, Rosetta was present when 67P reached its perihelion in August 2015. At this point, the comet was at its closest distance to the Sun (1.25 astronomical unit, while its mean distance is almost thrice this number), where the cometary activity is maximal.

The asteroids (2867) Šteins (left) and (21) Lutetia (right), seen by Rosetta. © ESA
The asteroids (2867) Šteins (left) and (21) Lutetia (right), seen by Rosetta. © ESA

So, Rosetta consisted of two modules: the orbiter itself, and the lander Philae. The orbiter had 11 instruments on board, and the lander 10. These instruments permitted, inter alia, to map the comet and measure its geometry, to constrain its internal structure and its chemistry, and to characterize its environment.

This environment is strongly affected by the Solar wind, especially in the vicinity of the perihelion, but not only.

The Solar wind

The Solar corona emits a stream of charges particles, which is mainly composed of electrons, protons, and alpha particles (kind of charged helium). This emission is called Solar wind. It is so energetic, that the emitted particles go far beyond the orbit of Pluto, constituting the heliosphere. The heliosphere has the shape of a bubble, and its boundary is called the heliopause. Voyager 1 crossed it in August 2012, at a distance of 121 AU of the Sun. At the heliopause, the pressure of the Solar wind is weak enough, to be balanced by the one of the interstellar medium, i.e. the winds from the surrounding stars. Hence, Voyager 1 is in this interstellar space, but technically still in the Solar System, as under the gravitational attraction of the Sun.

Anyway, our comet 67P/Churyumov-Gerasimenko is much closer than that, and has to deal with the Solar wind. Let us see how.

The physics of the interaction

Imagine you are on the comet, and you look at the Sun… which should make you blind. From that direction comes a stream of these charged particles (the Solar wind), and you can consider that their trajectories are parallel if far enough from the comet. Of course, the Sun does not emit on parallel trajectories, i.e. the trajectories of all these particles converge to the Sun. But from the comet, the incident particles appear to arrive on parallel trajectories.

While a charged particle approaches the comet, it tends to be deflected. Here, the dominating effect is not the gravitation, but the Lorentz force, i.e. the electromagnetic force. This force is proportional to the electric charge of the particle, and also involves its velocity, and the electric and magnetic fields of the comet.

The authors showed in a previous paper that the trajectories of the charged particles could be conveniently described in assuming that the magnetic field obeys an inverse-square law, i.e. its amplitude decreases with the square of the distance to the comet. If you are twice further from the comet, then the magnetic field is four times weaker.

I do not mean that the magnetic field indeed obeys this law. It is in fact more complex. I just mean that if you model it with such an ideal law, you are accurate enough to study the trajectories of the Solar wind particles. And this is what the authors did.

By the way, the authors suggest that any magnetic field following an inverse-power law could work. Of course, the numbers would have been different, but the global picture of the trajectories would be pretty much the same. It seems, at this time, too challenging to determine which of these models is the most accurate one.

Reducing the problem

The authors used analytical calculations, i.e. maths, which are in fact close to the classical ones, you make to show that the gravitation results in elliptic, parabolic, or hyperbolic, trajectories.

A wonderful tool assisting such studies is the First Integrals. A First Integral is a quantity, which remains constant all along a trajectory. For instance, in a gravitational problem where no energy is dissipated, then the total energy (kinetic + potential energies) is conserved. This is a First Integral. Another First Integral in that problem is the norm of the total angular momentum. And the existence of these two quantities helps to understand the shape of the possible orbits.

The authors showed that this is quite similar here. Even if the equations are slightly different (anyway the inverse-square law is a similarity), they showed that the problems has 2 First Integrals. And from these 2 First Integrals, they showed that knowing only 2 parameters is in fact enough to characterize the trajectories of the Solar wind particles. These two parameters are called rC and rE, they have the physical dimension of a distance, and are functions of all the parameters of the problems. rE characterizes the stream, it is related to its velocity, while rC characterizes a given particle. If you know just these 2 parameters, then you can determine the trajectory.

An empty cavity around the comet

The authors give a detailed description of the trajectories. To make things simple: either the particles orbit the comet, or they just pass by. But anyway, there is an empty space around the comet, i.e. a spherical cavity in which no Solar wind particle enters.

To come: comparison with in situ measurements

The journey of Rosetta around 67P crossed the boundary of this empty cavity. In other words, we have measurements of the density of charged particles at different distances from the comet, and also for different distances from the Sun, since the orbital phase of the mission lasted 2 years, during which 67P orbited the Sun. The authors promise us that a study of the comparison between the model and the in situ measurements, i.e. the observations, is to come. We stay tuned!

Rosetta does not operate anymore, and has landed (or crashed…) on 67P in September 2016. It is still there, and has on-board a kind of modern Rosetta stone. This is a micro-etched pure nickel prototype of the Rosetta disc donated by the Long Now Foundation, as part of its Rosetta Project. The disc was inscribed with 6,500 pages of language translations. This is a kind of time capsule, aiming at preserving part of our culture. Maybe someone will one day find 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.

Planets

Forming Mars

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Hi there! Of course, you know the planet Mars. You can here from it these days, since it is exceptionally close to our Earth. Don’t worry, this is a natural, geometrical phenomenon.

Anyway, it is a good time to observe it. But I will not speak of observing it, today. We will discuss its formation instead, because the issue of the formation of Mars remains a challenge. This is the opportunity to present The curious case of Mars’ formation, by James Man Yin Woo, Ramon Brasser, Soko Matsumura, Stephen J. Mojzsis, and Shigeru Ida. Astronomy and Astrophysics will publish it pretty soon.

Outline

Mars is too small
Forming planets from a disk
Two models of planetary formation
The composition challenge
Anticipating the composition
The study and its authors

Mars is too small

The following table gives you comparative characteristics of Venus, the Earth, and Mars.

Venus Earth Mars
Semimajor axis 0.723 AU 1.000 AU 1.524 AU
Eccentricity 0.007 0.017 0.093
Inclination 3.39° 0° 1.85°
Orbital period 224.7 d 365.25 d 686.96 d
Spin period -243.02 d 23.93 h 24.62 h
Mean diameter 12,104 km 12,742 km 6,779 km

The last line reveals a problem: Venus and the Earth are about the same size, while Mars is much smaller! But this is not the only problem: the compositions of the Earth and Mars are VERY different.

It is pretty easy to know the composition of the Earth: you just analyze samples. And for Mars? Just the same!

Interestingly, there are Martian meteorites on Earth. These are ejecta from impacts, which were ejected from Mars, and then traveled in the Solar System, until reaching our Earth.

In fact, over the tens of thousands of meteorites which have been found on Earth, a little more than one hundred were significantly different than the other ones, i.e. younger formation ages, a different oxygen isotopic composition, the presence of aqueous weathering products… Most of these meteorites were known as SNC, after the three groups they were classified into:

  • S for Shergottites, after the Shergotty meteorite (India, 1865),
  • N for Nakhlites, after the Nakhla meteorite (Egypt, 1911),
  • C for Chassignites, after the Chassigny meteorite (France, 1815).

Such a significant number of similar meteorites, which are that different from the other ones, suggests they come from a large body. Mars is an obvious candidate, which has been confirmed after the discovery that trapped gases in these meteorites are very similar to the ones, which are present in the atmosphere of Mars.

The Martian meteorite NWA (Northwest Africa) 2046, found in September 2003 in Algeria. This is a Shergottite. © Michael Farmer and Jim Strope.
The Martian meteorite NWA (Northwest Africa) 2046, found in September 2003 in Algeria. This is a Shergottite. © Michael Farmer and Jim Strope.

After that, the numerous space missions improved our knowledge of the Martian composition. And it finally appeared that both planets are essentially made of chondritic material. The Earth should accrete about 70% of enstatite chondrite (and same for the Moon), while Mars only about 50%. Chondrites are non-metallic meteorites, the enstatite chondrites being rich in the mineral enstatite (MgSiO3). These numbers are derived from the documented isotopic compositions of the Earth and Mars, i.e. the ratio of the different chemical elements. An isotope is a variant of a particular chemical element, which differs in neutron number.

If you want to convincingly simulate the formation of Mars, the product of your simulations should be similar to Mars in mass AND in composition. And this is very challenging. Let us see why, but first of all let us recall how to form planets from a disk.

Forming planets from a disk

At its early stage, a planetary system is composed of a proto-star, and a pretty flat disk, made of gas and dust. Then the dust accretes into clumps, which then collides to form planetary embryos, i.e. proto-planets. These embryos continue to grow with collisions, until forming the current planets. Meanwhile, the gas has dissipated.

Anyway, interactions between the protoplanets and between them and the gas can lead to planetary migration. This means that we cannot be sure whether the planets we know formed close to their current location. This makes room for several scenarios.

Two models of planetary formation

The obvious starting point is to assume that the planets formed close to their current locations. This so-called Classical model works pretty well for Venus, the Earth, Jupiter, Saturn… but not for Mars. The resulting Mars is too massive.

An idea for by-passing this problem is to start with a depletion of material at the location of Mars. This is equivalent to an excess inside the terrestrial orbit. In such a configuration, less material is available to the proto-Mars, which eventually has a mass, which is close to the present one.

You can get this excess of material inside the terrestrial orbit if you buy the Grand Tack scenario: when Jupiter formed, it created a gap in the inner disk, and the mutual interaction resulted in an inward migration of Jupiter, until reaching the present orbit of Mars. In moving inward (Type II migration), Jupiter pushed the material inward. Then, a 3:2 mean-motion resonance with Saturn occurred, which created another gap, and made Jupiter move outward, until its present location.

This way, you can form a planetary object, which is similar to Mars in mass and location.

But what about its composition?

The composition challenge

This is still a challenge. The composition of a planetary object is strongly affected by the one of the disk, where the object formed… which may not be its present location.

The authors added a free parameter to the model: the break location, which would split the protoplanetary disk into an inner and an outer region. The inner region would be rich in enstatite chondrites, while the outer one would be rich in ordinary chondrites.

A break location at 1.3 AU gives the best fit for the difference of composition between Mars and the Earth, for both formation scenarios (Classical and Grand Tack).

So, the Grand Tack with a break location at 1.3 AU could be the right scenario. But another possibility exists: the Classical scenario says that if Mars formed where it is, then it should be heavier. But what if Mars formed actually further from the Sun, and then migrated inward? Then, it would not need any depletion of material to have the right mass. And the break barrier should have been further than 1.3 AU. But you have to explain why it migrated inward.

Anticipating the composition

One of the good things with scenarios of formation is that thr gives more details on the outcomes, than actually observed. For instance, this study predicts the isotopic composition of 17O, 50Ti, 54Cr, 142Nd, 64Ni and 92Mo, in the Martian mantle. Further data, collected by space missions, will give additional constraints on these parameters, and test the validity of the present study. 8 missions are currently operational in orbit or on Mars, and InSight is en-route, after having been launched in May 2018. It should land on Mars on November 26, and will study its interior with a seismometer, and a heat transfer probe.

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.