Tag Archives: numerical methods

Forming Mars

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.

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° 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.

The Earth will encounter Apophis

Hi there! You may have heard of (99942) Apophis. As 2004 MN4, this Near-Earth Asteroid was considered to be a potential hazard. Don’t worry, it is not anymore. Anyway, it will have some close approaches with the Earth, the next one occurring in 2029. This makes it an interesting object, and the paper I present today deals with the way this close encounter will affect the rotation of Apophis. This study, Changes of spin axis and rate of the asteroid (99942) Apophis during the 2029 close encounter with Earth: a constrained model, led by Jean Souchay, has recently been accepted for publication in Astronomy and Astrophysics.

The asteroid (99942) Apophis

The asteroid (99942) Apophis has been discovered on June 19, 2004, and re-observed the day after (I should say the night, actually), at Kitt Peak Observatory in Arizona. It was then re-discovered six months later from Siding Spring Observatory, New South Wales, Australia, on December 18, and very soon confirmed that it was the same body. On December 27, it was realized that this object had actually already been observed in March. This precovery revealed to be very useful to determine its orbit. You can find below some of its characteristics:

Semi-major axis 0.9225867 AU
Eccentricity 0.1914717
Inclination 3.33687°
Period 323.5 d
Diameter ~350 m

Its orbital dynamics makes it a member of the group Aten. You can see that its orbital period is pretty close to the one of the Earth, i.e. close to one year. This raises the question: could it collide with our Earth? I answer NOT AT ALL, but the question was raised.

Potentially Hazardous Asteroids (PHAs)

Several programs, like NEODys in Italy, or the CNEOS in America, follow Near-Earth Asteroids which could possibly hit the Earth. Up to now, the identified PHAs have been proved to actually present no risk. The Torino scale categorizes the impact hazard associated with near-Earth objects, on a scale from 0 to 10. The risks of collisions and the energies involved are considered. 0 means no risk of impact, 5 means serious threat, 8 means certain collision… and 10 is the worst case, of course, which would characterize the Chicxulub impact, believed by most scientists to be a significant factor in the extinction of the dinosaurs. In such a case, the very existence of the human kind would be jeopardized.

The Minor Planet Center maintains a list of Potentially Hazardous Asteroids, i.e. worthwhile to be scrutinized. I currently count 1,923 of them, but this list is not static.

The observations of Apophis in December 2004 rated it at the level 4, which is a record since the creation of the Torino scale in 1999. Level 4 means that a collision with regional devastation has a probability of at least 1%. On December 27, 2004, the precovery images of Apophis dating from March have ruled out this possibility, and we now know that Apophis will not collide our Earth… or at least not before centuries. The next close approach will occur on April 13, 2029, at a distance of 38,400 km, which is about one tenth of the Earth-Moon distance. Such accurate numbers have been obtained after almost 15 years of astrometric observations of Apophis, which permitted to refine the dynamical models, i.e. fit the ephemerides.

A close encounter changes the dynamics

The mass ratio between the Earth and Apophis implies that, at such a small distance, Apophis will suffer from a huge kick of the Earth. This will drastically affect its dynamics, and would have significant implications for further predictions of its orbit. An accurate determination of the orbital changes requires to consider the non-sphericity of the Earth, the influence of the Sun and the Moon, and also non-gravitational forces, like the Yarkovsky effect. This is a thermal effect, due to the proximity of the Sun. It is barely constrained since it depends on the surface properties and the rotation of the body.
Of course, the future close approaches depend on the next ones. Another one will occur in 2036, its prediction will be much more accurate after the one of 2029.

A study by the same authors anticipate that the 2029 close encounter will affect the orbit of Apophis in such a way that it will move from the dynamical group of Aten to the one of Apollo. In particular, its semimajor axis will be close to 1.1 AU. As a consequence, its orbital period will lengthen from 324 to 422 days.

The rotation is critical

As I said, the Yarkovsky effect depends on the rotational state of Apophis. And this is probably why the study we discuss today deals with the rotation.
The rotation of Apophis has actually been studied in a recent past, from lightcurves. This is something I already discussed on this blog: in recording the Solar light, which is reflected by the surface of the body, you see variations, which are signatures of the rotational motion.

The lightcurves of Apophis revealed two main periods, at 27.38 h and 30.51 hours. The authors of that study (or here) interpreted these two periods as a combination between a fast precessional motion of the rotation axis, with a period of 27.38 h, and a slow and retrograde rotation, with a period of 263 h. This means that the rotation itself is slow and retrograde, but meanwhile the orientation of the North Pole of the body is moving some 10 times faster. Moreover, the authors discovered that the rotation axis was very close to the smallest figure axis. This is called Short-Axis Mode (SAM), and this means that the rotational energy is close to a minimum. In other words, some of it has been dissipated over the ages.

This is the currently observed rotation, but what will it be after the encounter?

A numerical study

The authors performed intensive numerical tests to answer this question. For that, they started from a set of 10,000 model-Apophis, all consistent with our current knowledge of the rotation of Apophis. In other words, these model-Apophis were oriented consistently with the uncertainties of the observations. They also considered the shape, which is itself derived from the lightcurves by Pravec et al. (2014).
Then, they propagated the rotation in using famous equations of the rigid rotation due to Kinoshita (1977), supplemented by a model of the tidal deformation of Apophis by the Earth, during its close approach. Then, the authors deduced the results from the statistics of the outcomes of their 10,000 numerical simulations.

Different obliquity, same spin rate

And here is the results: the authors find that the close encounter with the Earth should not significantly affect the spin rate of Apophis. However, the orientation of its spin axis will tend to align with the one of the Earth, affecting its obliquity.

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.

Locating Ultima Thule

Hi there! First I have to explain the title. Ultima Thule usually stands for any place beyond the known world… Actually, we will not leave the Solar System. Ultima Thule is an unofficial nickname for (486958) 2014 MU69, which is the next target of New Horizons spacecraft. Do you remember this spacecraft, which gave us outstanding images of Pluto and Charon in July 2015? That’s just the same one!
After having left Pluto, New Horizons changed its trajectory to 2014 MU69, which will be reached on January 1st, 2019. 6 months to wait then.
Interestingly, 2014 MU69 was unknown when New Horizons was launched in January 2006. Its primary mission was the binary Pluto-Charon and its satellites, and of course it was worth to extend the mission to another body. But choosing this second target was a difficult task, since the distant Solar System, here the Kuiper Belt, is very difficult to observe, and is pretty sparse. This is why observations programs of the Hubble Space Telescope (HST) were dedicated, and 2014 MU69 has been discovered in 2014.
Discovering an object is one thing, determining accurately its motion in view of a rendezvous with a spacecraft is another thing. This is the topic of the study I present today, High-precision orbit fitting and uncertainty analysis of (486958) 2014 MU69, by Simon Porter et al. This study has recently been published in The Astronomical Journal.

The New Horizons spacecraft

New Horizons is the first mission of NASA’s New Frontier program. It was launched in January 2006, and made its closest approach to Pluto in July 2015. Before that, it incidentally encountered the small asteroid (132524) APL at a distance of about 100,000 km in June 2006, and benefited from the gravitational assistance of Jupiter in February 2007.

The asteroid 132524 APL seen by New Horizons. © NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute
The asteroid 132524 APL seen by New Horizons. © NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute

It carries seven science instruments:

  • the Long-Range Reconnaissance Imager (LORRI), which images the encountered bodies,
  • the Solar Wind At Pluto (SWAP) instrument, which name is very explicit regarding its goal,
  • the Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI), which supplements SWAP for the detection of high-energy particles,
  • Alice, which is an ultraviolet imaging spectrometer,
  • the Ralph telescope, which is a photographic instrument,
  • the Venetia Burney Student Dust Counter (VBSDC) measures dust. This instrument has been built by students of the University of Colorado,
  • and the Radioscience Experiment (REX), which measured the temperature and the atmospheric pressure of Pluto.

As you can see from some of the names of the instrument, Pluto-Charon was definitely the primary goal of New Horizons. Anyway, Pluto is now behind, and New Horizons is en route to 2014 MU69, also nicknamed Ultima Thule.

Ultima Thule

At this time, our knowledge of Ultima Thule is very limited. This body has been discovered in 2014, from a dedicated observation program on the Hubble Space Telescope, to identify potential targets for New Horizons. Finally, 2014 MU69 has been selected, partly for technical reasons, i.e. it is not so difficult to reach from Pluto.

It was discovered in June 2014, and has an apparent magnitude of nearly 27, and an absolute one of 11. We can guess its size from its magnitude, and its diameter should be smaller than 50 km. So, a very small body. A stellar occultation happening in 2017 has revealed that its diameter should be closer to 25-30 km, and its shape may be bilobal, or it could even be a contact binary.

Observations of its dynamics revealed that it is a cold, classical Kuiper Belt object. Its eccentricity and inclination are limited, since they are not excited by any resonance with the giant planets. So, it belongs to a region of the Solar System, which is quiet from a dynamical point of view.

As I previously said, discovering it is not enough if you want a spacecraft to reach it. You must know its motion accurately, and for that you need more data. And Ultima Thule can be observed only with the Hubble Space Telescope.

Hubble Space Telescope data

The authors disposed of 5 observations of 2014 MU69, by the Wide Field Camera 3 (WFC3) of the HST. Even with the HST, imaging 2014 MU69 requires 6 minutes of exposure, i.e. you need to accumulate photons reflected by 2014 MU69 during 6 minutes to have enough signal.

The detection of 2014 MU<sub>69</sub>. © NASA, ESA, SwRI, JHU/APL, and the New Horizons KBO Search Team
The detection of 2014 MU<sub>69</sub>. © NASA, ESA, SwRI, JHU/APL, and the New Horizons KBO Search Team

Another difficulty comes from the number of stars in that region of the sky. This is due to the galactic latitude of 2014 MU69, which is close to 0, i.e. close to the Galactic plane. The images have to be treated, to remove their incoming light. This is not just a pixel, but a diffraction spot, which needs to be modeled to be properly removed.

Once you have these data, you can start to determine the orbit of 2014 MU69, i.e. make ephemerides.

From astrometry to orbit

When you catch a body on a 2-dimensional image of the sky, you get two coordinates. Basically, these coordinates translate into a right ascension, and a declination. And to build ephemerides of a body, you need to integrate the equation ruling the orbital motion. This equations is a second-order 3-dimensional ordinary differential equation.

The motion is ruled by the gravitational perturbation of the Sun and the major planets, and for the problem to be solved, you need initial conditions. These are a position and a velocity of 2014 MU69 at a given date, which you derive from your astrometric observations, i.e. the 5 couples (right ascension, declination).

Easy, isn’t it? No, it’s not! Because of the uncertainties on the measurements, your 10 data, i.e. 5 right ascensions and 5 declinations, do not exactly correspond to an initial condition. So, you have to make a fit, i.e. determine the initial condition, which best fits the observations.

There are many potential sources of uncertainties: the accuracy of the positioning of the HST, the accuracy of the coordinates of 2014 MU69 (remember: this is not a pixel, but a diffraction spot), the duration of the exposure… and also the location of the stars surrounding 2014 MU69 in the field of view. To make absolute astrometry, you need to know precisely the location of these stars, and you get their locations from a star catalogue. Currently, the astrometric satellite Gaia is making such a survey, with a never reached accuracy and comprehensiveness. The Gaia Data Release 2 has been released in April 2018, and gives positions and proper motions (i.e. you can now consider that the stars move from date to date) of more than 1 billion stars! The authors had the chance to use that catalogue. This resulted in predictions, which were accurate enough, to predict a stellar occultation, which has been observed from the Earth.

Predicting stellar occultations

When a Solar System body occultates a star, you can indirectly observe it. You observe the star with your telescope, and during a few seconds, the star disappears, and then reappears, because of this object, which light is too faint for you. Multiple observations of a stellar occultation give information on the motion of the object, and on its dimensions. The rings around Chariklo and Haumea have been discovered that way.

For 2014 MU69 (or Ultima Thule), an occultation has been successfully predicted. It has been observed 5 times on 2017 July 17, in Argentina, giving 5 solid-body chords. This permitted us to infer that 2014 MU69 could be bilobal, or even a contact binary.

A stable orbit

And from these astrometric data, the authors propagated the orbit of 2014 MU69 over 100 million years, in considering the uncertainties on the initial positions. The outcomes of the simulations safely state that 2014 MU69 is on a very stable orbit, with a mean semimajor axis of 44.23 astronomical units (39.48 for Pluto), and an orbital eccentricity smaller than 0.04. This results in an orbital period of 294 years, during which the distance to the Sun barely varies.

We are looking forward for the encounter in 6 months!

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.

Evolution of Venus’ crust

Hi there! Of course, you know Venus. This planet is sometimes nicknamed the twin sister of the Earth, but beside its size, it does not look like the Earth. Venus is closer to the Sun than us, and it has a very thick atmosphere, which is essentially composed of carbon dioxide. This atmosphere has a pressure of 93 bar at the surface of the planet, to be compared with 1 bar for the Earth, and the temperature reaches there 470°C. Definitely hostile.

Anyway, I do not speak of the atmosphere today, but of the surface. I present Inferences on the mantle viscosity structure and the post-overturn evolutionary state of Venus, by T. Rolf and collaborators, which has recently been published in Icarus.

The interior of Venus

Given its size, i.e. a diameter of 12,000 km, which is 95% of the one of the Earth, Venus must be differentiated. It has a crust, a mantle, and core, with increasing densities when you go deeper below the surface. We think the crust to be essentially basaltic, while the core must contain heavy elements. Surprisingly, the space missions did not detect any magnetic field, which means that the core may be not solid, or may be not cooling…

The outer part of the mantle should be fluid, which means that a fluid layer separates the core from the mantle. We know very few of the thicknesses and the compositions of these different layers. Actually, these could only be guessed from the measurements we dispose on, which are the gravity and the topography (see just below). Once you know the gravity field of Venus and its topography, you can elaborate interior models, which would be consistent with your data.

Gravity and topography

First, gravity. When a small body, like an artificial satellite, orbits a spherical planetary body, the gravitational perturbation affecting its motion depends only on the distance between the satellite and the planet. Now, if the planet is not spherical, and has mass anomalies, then the perturbation will not only depend on the distance, but also on the direction planet-satellite. You can determine the gravity field from the orbital deviation of your spacecraft.

It is convenient to write the gravity field as a sum of spherical harmonics. The first term (order 0) is a spherical one, then the order 2 (you have no order 1 if the center of your reference frame is the center of mass) represents the triaxiality of the planet, i.e. the planet seen as a triaxial ellipsoid. And the higher order terms will represent anomalies, with increasing resolutions. These resolutions are modeled as spatial periods. Such a representation has usually an efficient convergence, except for highly elongated bodies (see here).

We use such a representation for the topography as well. The difference is that the result is not the gravity field in any direction, but the altitude of the surface for a given point, i.e. a latitude and a longitude. The spacecraft measure the topography with a laser, which echo gives you the distance between the spacecraft and the surface. The altitude is directly deduced from this information.

Topography of Venus. The altitude variations are about 13 km with respect to a reference ellipsoid. © Calvin Hamilton, Johns Hopkins University Applied Physics Laboratory
Topography of Venus. The altitude variations are about 13 km with respect to a reference ellipsoid. © Calvin Hamilton, Johns Hopkins University Applied Physics Laboratory

The best representations we dispose on for Venus come from the American spacecraft Magellan, which orbited Venus between 1990 and 1994. These representations go to the order 180.

Modeling the crustal evolution

In this study, the authors simulated possible evolutionary paths for the crust of Venus, and compared their results with the present Venus, i.e. the gravity and topography as we know them.

For that, they simulated the thermochemical evolution of Venus in using a numerical code, StagYY. This is a 3D-code, which models convection in the mantle, i.e. internal motions. This code is based on finite elements, i.e. the interior of Venus is split into small elements. This splitting is made following a so-called Yin-Yang grid, which is appropriate for spherical geometries. This code includes several features like phase transition (i.e. from solid to fluid, and conversely), compositional variations, partial melting and melt migration. Moreover, it is implemented for parallel computing.

In other words, these are huge calculations. The authors started with 10 simulations in which the crust was modeled as a single plate, i.e. a stagnant lid. The simulations differed by the modeling of the viscosity, and by the radiogenic heating rate. This is the heating of Venus by the decay of the radiogenic elements, which was most effective in the early Solar System.

Once these 10 simulations have run, the authors kept the one, which resulted in the closest Venus to the actual one, and introduced episodic overturns in it.

Stagnant-lid vs. overturn

Venus does not present any tectonic activity. Did it have some in the past? This is a question this study tried to answer.

An overturn is a sudden peak in the heat transfer from the core to the crust through the mantle, due to a too strong difference of temperature, i.e. when the mantle gets colder. Such an episodic phenomenon is triggered by a too thick crust, and results in a melting of this crust, in heating it. In other words, it regulates the thickness of the crust.

Overturns should have happened

And here are the results: the best stagnant-lid scenario, called S2 in the study, presents some discrepancy between the simulated present Venus and the observed one. These discrepancies are present in the topography, in the gravity field, and in the age of the surface. The surface is estimated to be between 0.3 and 1 Gyr old, while the best stagnant-lid scenario predicts that the most probable age is 0.25 Gyr… a little too young.

However, episodic overturns give a surface, which is 0.6 Gyr old. Moreover, the gravity and topography are much better fit. The only remaining problem is that this scenario should result in much detections of plumes than actually detected.

As the authors honestly recall, some physical phenomena were not considered, in particular the influence of the dense atmosphere, and intrusive volcanism. Anyway, this study strongly suggests that episodic overturn happened.

Further data will improve our understanding of Venus. Recently, the European Space Agency (ESA) has pre-selected 3 potential future space missions, including EnVision, i.e. an orbiter around Venus. The final decision is expected in 2021.

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.

Saturn sends us meteorites

Hi there! First I would like to thank you for following me on Facebook. The Planetary Mechanics page has reached 1,000 followers!

OK, now back to business. Did you know that our Earth is intensively bombarded from space? You have recently heard of this Chinese space station, Tiangong-1… in that case, it was man-made stuff. But we are intensively bombarded by natural space material. Most of it is so small that it is destroyed when entering the atmosphere, but sometimes it arrives to us as stones… And in extreme cases, the impactor is so large that its impact may generate an extinction event. The Chicxulub crater, in Mexico, is thought to result from the impact, which aftermath provoked the extinction of the dinosaurs, some 66 Myr ago.

The meteorites I speak about today are the ones, which fall on the Earth every year. This is the opportunity to discuss about Identification of meteorite source regions in the Solar System, which has recently been accepted for publication in Icarus. In that study, the authors determine the origin of 25 meteorites, from their observed trajectories just before they hit us.

Meteorites bombard the Earth

We estimate that currently 60 tons of cosmic material fall on the Earth every day. This seems huge, but actually most of it arrives to us as dust, since the original object does not survive its entry into the atmosphere. In fact, the larger the meteorite, the less frequent it falls on us. 4-m objects arrive every ~16 months, 10-m ones every ~10 years, and 100-m ones every ~5,200 years. And they arrive somewhere on Earth… do not forget that most of the surface of our planet is water. So, don’t worry.

The contact of such a small object with the atmosphere may generate an airburst, which itself could be detected, in many frequencies. I mean, you may hear it, you may see it (make a wish), it can also disturb the radio emissions. This motivated the existence of several observation programs, dedicated to the detection of meteors.

Observation networks

Programs of observation exist at least since 1959, originally under the impulse of Ondřejov Observatory (Czech Republic). These are usually national programs, e.g.

and there are probably more. These are networks of camera, which systematically record the sky, accumulating data which are then automatically treated to detect meteors. The detection of a meteors from different location permit to determine its trajectory.

Detection of a fireball by FRIPON, in September 2016. © FRIPON
Detection of a fireball by FRIPON, in September 2016. © FRIPON

Identifying the source

As I said, multiple detections, at different locations, of a fireball, permit to derive its trajectory. This trajectory gives in particular the radiant, which is the direction from which the meteorite, or the impactor, seems to come. The authors are also interested in the velocity of the object.

The velocity and the radiant are determined with respect to the Earth. Once they are determined, the authors translated them into heliocentric elements, i.e. they determined the pre-impact trajectory of the object with respect to the Sun. And this makes sense, since Solar System objects orbit the Sun! This trajectory is made of orbital elements, i.e. semimajor axis, eccentricity, inclination, and the uncertainties associated. Don’t forget that the observations have an accuracy, which you must consider when you use the data. The magnitude of the fireball tells us something on the size of the impactor as well.

From these data, the authors wondered from where the object should come from.

7 candidates as reservoirs of meteorites

The authors identified 7 possible sources for these impactors. These regions are the densest parts of the Main Asteroid Belt.
These are:

  1. the Hungaria family. These asteroids have a semimajor axis between 1.78 and 2 astronomical units, and an inclination between 16° and 34° with respect to the ecliptic, i.e. the orbit of the Earth,
  2. the ν6 resonance: these are bodies, which eccentricity raise because excited by Saturn. They orbit at a location, where they are sensitive to the precessional motion of the pericentre of Saturn. The raise of their eccentricity make these bodies unstable, and good candidates for Earth-crossers. Their semimajor axis is slightly smaller than 2 AU.
  3. the Phocaea family: this is a collisional family of stony asteroids. Their semimajor axes lie between 2.25 and 2.5 AU, their eccentricities are larger than 0.1, and their inclinations are between 18° and 32°. They are known to be a source of Mars-crossers.
  4. the 3:1 MMR (mean-motion resonance with Jupiter): these bodies perform exactly 3 orbits around the Sun while Jupiter makes one. They lie at 2.5 AU. The perturbation by Jupiter tends to empty this zone, which is called a Kirkwood gap.
  5. the 5:2 MMR, at 2.82 AU. This is another Kirkwood gap.
  6. the 2:1 MMR, at 3.27 AU, also known as Hecuba gap,
  7. the Jupiter Family Comets. These are comets, which orbital periods around the Sun are shorter than 20 years, and which inclinations are smaller than 30° with respect to the ecliptic. They are likely to be significantly perturbed by Jupiter.

For each of the 25 referenced meteorites, the authors computed the probability of each of these regions to be the source, in considering the orbital elements (semimajor axis, eccentricity, and inclination) and the magnitude of the object. Indeed, the magnitude is correlated with the size, which is itself correlated with the material constituting it. The reason is that these Earth-crossers orbit the Sun on eccentric orbits, and at their pericentre, i.e. the closest approach to the Sun, they experience tides, which threaten their very existence. In other words, they might be disrupted. Particularly, a large body made of weak material cannot survive.

And now, the results!

Saturn send meteorites to the Earth!

The authors find that the most probable source for the meteorites is the ν6 secular resonance, i.e. with Saturn. In other words, Saturn sends meteorites to the Earth! Beside this, the Hungaria family and the 3:1 mean-motion resonance with Jupiter are probable sources as well. On the contrary, you can forget the Phocaea family and the 2:1 MMR as possible sources.
It appears that the inner belt is more likely to be the source of meteorites than the outer one. Actually, the outer belt mostly contains carbonaceous asteroids, which produce weak meteoroids.

The authors honestly recall that previous studies found similar results. Theirs also contains an analysis of the influence of the uncertainty on the trajectories, and of the impact velocity with the Earth. This influence appears to be pretty marginal.

Anyway, the future will benefit from more data, i.e. more detections and trajectory recoveries. So, additional results are to be expected, just be patient!

The study and its authors

  • You can find the study here, on the website of Icarus. This study is in open access, which means that the authors paid extra fees to make the study available to us. Many thanks to them!
  • You can visit here the website of Mikael Granvik, the first author of the study,
  • and the one of the second author, Peter Brown.

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