Tag Archives: comets

Origin of the ecliptic comets

Hi there! Today we discuss the ecliptic comets. You know the comets, these dirty snowballs which show two tails when they approach the Earth (in fact, they have a tail because they approach the Sun). The study I present today, The contribution of dwarf planets to the origin of low-inclination comets by the replenishment of mean motion resonances in debris disks, by M.A. Muñoz-Gutiérrez, A. Peimbert & B. Pichardo, tells us on the dynamical origin of those of these bodies, which have a low inclination with respect to the orbit of the Earth (the ecliptic). Simulations of their own of the primordial debris disk beyond Neptune show that the presence of dwarf planets, like Eris or Haumea, supplies future ecliptic comets. This study has recently been published in The Astronomical Journal.

The dynamics of comets

As I said, comets are dirty snowballs. They are composed of a nucleus, made of ice and silicates. When the comet approaches the Sun, it becomes hot enough to sublimate the ice. This results in two visible tails: a dusty one, and a tail of ionized particles. Beside this, there is a envelope of hydrogen, and sometimes an antitail, which direction is opposite to the dusty tail.

The comets usually have a highly eccentric orbit. As a consequence, there are huge variations of the distance with the Sun, and this is why their activity is episodic. Their temperature increases with the closeness to the Sun, triggering outgassing.

In fact, a moderately eccentric body may be considered to be a comet, if activity is detected. This is for instance the case of the Centaur Chiron. Chiron was detected as an asteroid, and later, observations permitted to detect a cometary activity, even if it does not approach the Sun that much. But of course, this does not make the kind of beautiful comets that the amateur astronomers love to observe.

Regarding the “classical” comets: they have a high eccentricity. What does raise it? The study addresses this question. But before that, let us talk about the ecliptic comets.

The ecliptic comets

The ecliptic comets are comets with a low inclination with respect to the orbital plane of the Earth. In fact, the detections of comets have shown that they may have any inclination. The ecliptic comets are an interesting case, since they are the likeliest to approach the Earth (don’t worry, I don’t mean collision… just opportunities to observe beautiful tails 😉 ).

These low inclinations could suggest that they do not originate from the Oort cloud, but from a closer belt, i.e. the Kuiper Belt. You know, this belt of small bodies which orbits beyond the orbit of Neptune. The reason is that part of this belt has a low inclination.

It also appears that beyond the orbit of Neptune, you have dwarf planets, i.e. pretty massive objects, which are part of the Trans-Neptunian Objects. The authors emphasize their role in the dynamics of low-inclination comets.

Dwarf planets beyond Neptune

A dwarf planet is a planetary object, which does not orbit another planet (unlike our Moon), and which is large enough, to have a hydrostatic shape, i.e. it is pretty spherical. But, this is not one of the planets of the Solar System… you see it is partly defined by what it is not…

5 Solar System objects are officially classified as dwarf planets. 3 of them are in the Kuiper Belt (Pluto, Haumea and Makemake), while the other two are the Main-Belt asteroid Ceres, and Eris, which is a Trans-Neptunian Object, but belongs to the scattered disc. In other words, it orbits further than the Kuiper Belt. The following table presents some characteristics of the dwarf planets of the Kuiper Belt. I have added 4 bodies, which may one day be classified as dwarf planets. Astronomers have advised the IAU (International Astronomical Union) to do so.

Semi-major axis Eccentricity Inclination Orbital period Diameter
Pluto 39.48 AU 0.249 17.14° 248.09 yr 2,380 km
Haumea 43.13 AU 0.195 28.22° 283.28 yr ≈1,500 km
Makemake 45.79 AU 0.159 28.96° 309.9 yr 1,430 km
Orcus 39.17 AU 0.227 20.57° 245.18 yr 917 km
2002 MS4 41.93 AU 0.141 17.69° 271.53 yr 934 km
Salacia 42.19 AU 0.103 23.94° 274.03 yr 854 km
Quaoar 43.41 AU 0.039 8.00° 285.97 yr 1,110 km

Anyway, the dynamical influence of a planetary object does not depend on whether it is classified or not.

These are objects, which have a significant mass, orbiting in the Kuiper Belt. And they are involved in the study.

The Solar System originates from a disc

The early Solar System was probably made of a disk of small bodies, which formed after the gravitational collapse of a huge molecular cloud. Then the Sun accreted, planets accreted, which destabilized most of the remaining small bodies. Some of them where just ejected, some bombarded the Sun and the planets, some other accreted…

Here the authors work with the Kuiper Belt as a disc. So, they assume the 8 major planets to be formed. Moreover, they already have dwarf planets in the disc. And the small bodies, which are likely to become comets, are under the gravitational influence of all this population of larger bodies.

For them to become comets, their eccentricities have to be raised. And an efficient mechanism for that is resonant excitation.

Eccentricity excitation by Mean-Motion Resonances (MMR)

A mean-motion resonance (MMR) between two bodies happens when their orbital periods are commensurate. In the present case, the authors considered the 2:3 and 1:2 MMR with Neptune. The 2:3 resonance goes like this: when Neptune makes 3 orbital revolutions around the Sun, the small object makes exactly 2. And when an object makes one revolution while Neptune makes 2, then this object is at the 1:2 MMR. These two resonances are in the Kuiper Belt disc considered by the authors.

Such period ratios imply that the small bodies orbit much further than Neptune. Neptune orbits at 30.1 AU (astronomical units) of the Sun, so the 2:3 MMR is at 39.4 AU (where is Pluto), and the 2:1 MMR is at 47.7 AU.

When a small body is trapped into a MMR with a very massive one, the gravitational perturbation accumulates because of the resonant configuration. And this interaction is the strongest when the two bodies are the closest, i.e. when the small body reaches its perihelion… which periodically meets the perihelion of the massive perturber, since it s resonant. So, the accumulation of the perturbation distorts the orbit, raises its eccentricity… and you have a comet!

But the issue is: in raising the eccentricities, you empty the resonance… So, either you replenish it, or one day you have no comet anymore… Fortunately, the authors found a way to replenish it.

Numerical simulations

The authors ran different intensive numerical simulations of multiple disc particles, which are perturbed by Neptune and dwarf planets. These dwarf planets are randomly located. They challenged different disc masses, the masses of the dwarf planets being proportional to the total mass of the disc.

And now, the results!

Replenishment of the 2:1 Mean-Motion Resonance (MMR)

The authors found nothing interesting for the 3:2 MMR. However, they found that the presence of the dwarf planets replenishes the 2:1 MMR. So here is the process:

  1. When a particle (a km-size body) is trapped into the 2:1 MMR, its eccentricity is raised
  2. It becomes a comet and may be destabilized. It could also become a Jupiter-family comet, i.e. a comet which period is close to the one of Jupiter. This happens after a close encounter with Jupiter.
  3. Other particles arrive in the resonances, and become comets themselves.

One tenth of the ecliptic comets

The authors also estimated the cometary flux, which this process should create. The authors estimate that it can give up to 8 Jupiter-family comets in 10,000 years, while the observations suggest a ten times larger number.
So, this is a mechanism, but probably not the only one.

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.

When a comet meets the Solar wind

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.

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.

An active asteroid

Hi there! Today we will detail a recent study by Jessica Agarwal and Michael Mommert, entitled Nucleus of active asteroid 358P/Pan-STARRS (P/2012 T1). This study has recently been accepted for publication in Astronomy and Astrophysics, and consists in increasing our knowledge of a recently discovered object, i.e. P/2012 T1. This object proved to have some activity, like a comet. The authors realized several observations to try to characterize its activity, and infer some physical properties like its size and its rotation.

Comet vs. active asteroid

First of all, I would like to make clear what is a comet, and what is an active asteroid. I am very ambitious here, since these two notions actually overlap. For instance, our object is both an active asteroid, and a main-belt comet.

Let us say that a comet is an active asteroid, while an active asteroid is not necessarily a comet. The difference is in the nature of the activity.

A comet is a dirty snowball, i.e. you have water ice, and some silicates. Its orbit around the Sun is usually pretty eccentric, so that you have large variations of the distance Sun-object. The location of the orbit, at which the distance is the smallest, is called pericentre. When the comet approaches the pericentre, it approaches the Sun, heats, and part of its water ice sublimates. This results in a dusty tail (actually there are two tails, one being composed of ionized particles).

But when you see dust around a small body, i.e. when you see activity, this is not necessarily ice sublimation. There could be for instance rock excavated by an impact, or material expelled by fast rotation. In that case, you still have an active asteroid, but not a comet. One of the goals of this study is to address the cause and nature of P/2012 T1’s activity.

The asteroid P/2012 T1

P/2012 T1, now named 358P, has been discovered in October 2012 by the Pan-STARRS-1 survey. Pan-STARRS stands for Panoramic Survey Telescope and Rapid Response System, it uses dedicated facilities at Haleakala Observatory, Hawaii, USA.

Discovery of P/2012 T1. © Pan-STARRS
Discovery of P/2012 T1. © Pan-STARRS

Its provisional name, P/2012 T1, contains information on the nature of the object, and its discovery. P stands for periodic comet, 2012 is the year of the discovery, and T means that it has been discovered during the first half of October.

Interestingly, this object appeared on images taken in December 2001 at Palomar Observatory in California, while acquiring data for the survey NEAT (Near-Earth Asteroid Tracking).

You can find below its orbital elements, from the Minor Planet Center:

Semi-major axis 3.1504519 AU
Eccentricity 0.2375768
Inclination 11.05645°
Period 5.59 y

From its orbital dynamics, it is a Main-Belt object. As a comet, it is a Main-Belt Comet.

New observations

Once an object is known and we know where it is, it is much easier to reobserve it. The authors conducted observations of 358P from the Southern Astrophysical Research (SOAR) telescope, and the Very Large Telescope.

The SOAR telescope is based on Cerro Pachón, Chile. This is a 4.1-m aperture facility, located at an altitude of 2,700 m. The authors took images with the Goodman High Throughput Spectrograph during one night, from July 27 to July 28, 2017. They wanted to analyze the reflected light by the asteroid at different wavelengths, unfortunately the observational constraints, i.e. cloud coverage, permitted only two hours of observations. Only the observations made with the VR filter, centered at 610 nm, were useful.

These data were supplemented by 77 images taken during 10 hours from August 17 to August 18, 2017, at the Very Large Telescope. This instrument depends on the European Southern Observatory (ESO), and is located on Cerro Paranal, once more in Chile, at an altitude of 2,635 m. The authors used the FOcal Reducer and low dispersion Spectrograph 2 (FORS2), which central wavelength is 655 nm.

The observations give raw images. The authors treated them to get reliable photometric and astrometric measurements of 358P, i.e. they corrected from the variations of the luminosity of the sky, in using reference stars, and from the possible instrumental problems. For that, they recorded the response of the instrument to a surface of uniform brightness, and used the outcome to correct their images.

Let us now address the results.

Measuring its rotation

Such a small (sub-kilometric) body is not spherical. This results in variations of luminosity, which depend on the surface element which is actually facing your telescope. If you acquire data during several spin periods of the asteroid, then you should see some periodicity in the recorded lightcurve.

The best way to extract the periods is to make a Fourier transform. Your input is the time-dependent lightcurve you have recorded, and your output is a frequency-dependent curve, which should emphasize the periods, which are present in the recorded lightcurve. If the signal is truly periodic, then it should exhibit a maximum at its period and its harmonics (i.e. twice the period, thrice the period, etc.), and almost 0 outside (not exactly 0 since you always have some noise).

In the case of 358P, the authors did not identify any clear period. A maximum is present for a rotation period of 8 hours, but the result is too noisy to be conclusive. A possible explanation could be that we have a polar view of the asteroid. Another possibility is that the albedo of the asteroid (the fraction of reflected light) is almost uniform.

Dust emission

The authors tried to detect debris around the nucleus of the comet, in widening the aperture over which the photometry was performed. They got no real detection, which tends to rule out the possibility of non-cometary activity.

A 530m-large body

Finally, the magnitude of the asteroid is the one of a sphere of 530 meters in diameter, with an albedo of 6%. This means that a higher albedo would give a smaller size, and conversely. The albedo depends on the composition of the asteroid, which is unknown, and can be only inferred from other asteroids. The authors assumed it to be a carbonaceous asteroid (C-type), as 75% of the asteroids. If it were an S-type (silicateous) body, then it would be brighter. A wide band spectrum of the reflected light would give us this information.

The study and its authors

  • You can find the study here, on Astronomy and Astrophysics’ website. Moreover, the authors uploaded a free version on arXiv, thanks to them for sharing!
  • Here is the webpage of the first author, Jessica Agarwal,
  • and here the website of Michael Mommert.

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 activity of Chiron

Hi there! You may have heard of Chiron, which was he first Centaur discovered, in 1977. This minor planet may have rings, and seems to present some cometary activity, which cause needs to be discussed. This is the topic of the present study, i.e. Activity of (2060) Chiron possibly caused by impacts?, by Stefan Cikota, Estela Fernández-Valenzuela, Jose Luis Ortiz, Nicolás Morales, René Duffard, Jesus Aceituno, Aleksandar Cikota and Pablo Santos-Sanz. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

Chiron’s facts

Chiron was the first discovered Centaur, i.e. the first asteroid / small planet, which orbits between the orbits of Saturn and Uranus. It was discovered in 1977, in the sense that it was identified in 1977. But reexamination of past photographic plates show that it has in fact been observed since 1895. And from the reanalysis of the pre-discovery observations, it was easy to determine an orbit.

Discovery 1977
First observation 1895
Apparent magnitude 19
Absolute magnitude 6
Diameter 220 km
Semimajor axis 13.648 AU
Eccentricity 0.3823
Inclination 6.9497°
Orbital period 50.42 yr
Rotation 5.918 h

The orbital period of Chiron is a slightly longer than 50 years, which means that we dispose of astrometric observations over more than 2 periods. This orbit is highly eccentric, which results in large variations of the distance to the Sun, i.e. between 8.43 AU (astronomical units) at perihelion, and 18.86 AU at aphelion.

A spectral analysis of Chiron reveals a C-type, i.e. a carbonaceous, object. Moreover, it shows large variations of brightness, which are considered to be partly due to cometary activity, and partly due to rings. This cometary activity makes that Chiron, officially the asteroid (2060)Chiron, can also be called the comet 95P/Chiron.

Chiron observed at Kuma Kogen Astronomical Observatory, Japan. © 1997 by Akimasa Nakamura
Chiron observed at Kuma Kogen Astronomical Observatory, Japan. © 1997 by Akimasa Nakamura

The presence of rings around Chiron is not unanimously accepted in the scientific community. Unexpected stellar occultations by something orbiting close to Chiron could be interpreted either as cometary jets, or as rings. But the large variations of brightness and the discoveries of rings around Chariklo and Haumea speak for the presence of rings. The discovery of rings around Chariklo was very surprising, and showed that it is possible. The discovery around Haumea has shown that rings around such bodies were not exceptional. So, why not Chiron? In this study, the authors clearly state that they believe in the presence of rings, and they use it to study the brightness of Chiron. These rings would have a radius of 324 ± 10 km, which is inside the estimated Roche limit of Chiron, i.e. the particles constituting the rings could not accrete into a larger body.

But the central point is the cometary activity, i.e. evidence for cometary jets is reported.

Triggering a cometary activity

Classical comets behave this way: these are dirty snowballs, i.e. made of ice, dust, and some other elements. When approaching the Sun, the comet gets so warm that the ice is sublimated. But a Centaur with cometary activity is different, since it does not get closer to the Sun. Moreover, Chiron is essentially carbonaceous. So, another cause has to be found. And in such a case, it is often tempting to invoke impacts.

A problem is that impacts are not that frequent in that region of the Solar System. First because the gravitational action of the Sun tends to focus the orbits of the potential impactors, i.e. they will be more inclined to get closer to the Sun, and second because, the more distant from the Sun you are, the emptier the space appears, this is just a geometrical effect.
The consequences of these effects is that a collision of a 1km-radius comet is expected on a body like Chiron every 60 Gyr… while the age of the Solar System is 4.5 Gyr… quite unlikely.

Photometric observations

Anyway, Chiron is known to have some cometary activity, and the author tracked it from Calar Alto Observatory (CAHA) in Almeria, Spain, during 3 observation campaigns, between 2014 and 2016. The first campaign was primarily devoted to the study of the rotation of Chiron, and consisted of 3 runs in 2014, using the 3.5 and the 1.23 m telescopes. The second campaign was conducted in September 2015 on the 2.2 m telescope, with the CAFOS instrument (Calar Alto Faint Object Spectrograph), and looked for rotation, absolute magnitude, and cometary activity. The third campaign took place on 2016, September 2, to get a better constraint on Chiron’s absolute magnitude, once again with CAFOS.

The authors were particularly interested in the photometry, since cometary jets translate into variations of brightness. For that, they had to correct the variations due to observational constraints, and to the orientation of Chiron.

The 3.5m telescope at Calar Alto Observatory (CAHA). © Alfredo Madrigal
The 3.5m telescope at Calar Alto Observatory (CAHA). © Alfredo Madrigal

Observational constraints are likely to give artificial variations of photometry, since

  • the height of Chiron on the horizon varies, which means that the thickness of the atmosphere varies,
  • the wind might result in unstable images (seeing),
  • the detectors are different, even on the same instrument,etc.

To try to make things as proper as possible, the authors corrected the images from flat fielding, i.e. from the variations of the response of the CCD chip, and they observed a large enough field (at least 16 arcmin), to have the same stars as photometric references.

Regarding the orientation of Chiron, variations of brightness can reveal:

  • the rotation of Chiron, which would present different surface elements to the observer,
  • the orientation of the rings.

These two effects were modeled, to be removed from the photometric measurements. And the result is…

Impacts from the rings

The authors do observe a small cometary activity on Chiron, which is pretty faint. It has actually been stronger in the past, a measurement in 1973 showed a peak with respect to another measurement in 1970, and since then the coma is monotonously decreasing. The authors interpret that as a possible small impact having occurred between 1970 and 1973, the associated coma tail having almost disappeared. This activity appears to be supplemented by a continuous micro-activity, which could be due to impacts by small particles falling from the rings.

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.

Breaking an asteroid

Hi there! Asteroids, these small bodies in the Solar System, are fascinating by the diversity of their shapes. This is a consequence of their small sizes. Another consequence is their weakness, which itself helps to split some of them into different parts, sometimes creating binary objects, asteroids families… The study I present you today, Internal gravity, self-energy, and disruption of comets and asteroids, by Anthony R. Dobrovolskis and Donald G. Korycansky, proposes an accurate computation of the required energy to provoke this break-up, at any place of the asteroid, i.e. you are more efficient when you hit at a given location. This study has recently been accepted for publication in Icarus.

Shapes of asteroids

Please allow me, in this context, to call asteroid a comet, a comet being a small body, i.e. like an asteroid, but with a cometary activity. The important thing is that the involved bodies are small enough.

Beyond a given size, i.e. a diameter of ~400 km, a planetary body is roughly spheroidal, i.e. it is an ellipsoid with it two equatorial axes almost equal and the polar one smaller, because of its rotation. For a tidally despun body, like the Moon, or a satellite of a giant planet, the shape is more triaxial, since the tidal (gravitational) action of the parent planet tends to elongate the equatorial plane. The same phenomenon affects Mercury.

However, for smaller bodies, the self-gravitation is not strong enough to make the body look more or less like a sphere. As a consequence, you can have almost any shape, some bodies are bilobate, some are contact binaries, i.e. two bodies which permanently touch together, some others are rubble piles, i.e. are weak aggregates of rocks, with many voids.

These configurations make these bodies likely to undergo or have undergone break-up. This can be quantified by the required energy to extract some material from the asteroid.

The energies involved

For that, an energy budget must be performed. The relevant energies to consider are:

  • The impact disruption energy: the minimum kinetic energy of an impactor, to shatter the asteroid and remove at least half of its mass,
  • The shattering energy: the minimum energy needed to shatter the asteroid into many small pieces. It is part of the impact disruption energy. This energy is roughly proportional to the mass of the asteroid. It represents the cohesion between the adjacent pieces.
  • The binding energy: this energy binds the pieces constituting the asteroid. In other words, once you have broken an asteroid (don’t try this at home!), you have to make sure the pieces will not re-aggregate… because of the binding energy. For that, you have to bring enough energy to disperse the fragments.
  • The self-gravitational energy: due to the mutual gravitational interaction between the blocks constituting the asteroids. Bodies smaller than 1 km are strength-dominated, i.e. they exist thanks to the cohesion between the blocks, which is the shatter energy. However, larger bodies are gravity-dominated.
  • The kinetic energy of rotation: the spin of these bodies tends to enlarge the equatorial section. In that sense, it assists the break-up process.

This study addresses bodies, which are far enough from the Sun. This is the reason why I do not mention its influences, i.e. the tides and the thermic effects, which could be relevant for Near-Earth Objects. In particular, the YORP effect is responsible for the fission of some of them. I do not mention the orbital kinetic energy of the asteroid either. Actually the orbital motion is part of the input energy brought by an impact, since the relative velocity of the impactor with respect to the target is relevant in this calculation.

I now focus on the two cases studied by the authors to illustrate their theory: the asteroid Kleopatra and the comet 67P/Churyumov-Gerasimenko.

2 peculiar cases: Kleopatra and Churyumov-Gerasimenko

216 Kleopatra is a Main-Belt asteroid. Adaptive optics observations have shown that is is constituted of two masses bound by material, giving a ham-bone shaped. As such, it can be considered as a contact binary. It is probably a rubble pile. Interestingly, observations have also shown that Kleopatra has 2 small satellites, Alexhelios and Cleoselene, which were discovered in 2008.

Reconstruction of the shape of Kleopatra. © NASA
Reconstruction of the shape of Kleopatra. © NASA

However, 67P Churyumov-Gerasimenko is a Jupiter-family comet, i.e. its aphelion is close to the orbit of Jupiter, while its perihelion is close to the one of the Earth. It has an orbital period of 6.45 years, and was the target of the Rosetta mission, which consisted of an orbiter and a lander, Philae. Rosetta orbited Churyumov-Gerasimenko between 2014 and 2016. The shape of this comet is sometimes described as rubber ducky, with two dominant masses, a torso and a head, bound together by some material, i.e. a neck.

Churyumov-Gerasimenko seen by Rosetta. © ESA
Churyumov-Gerasimenko seen by Rosetta. © ESA
216 Kleopatra 67P/Churyumov-Gerasimenko
Semimajor axis 2.794 AU 3.465 AU
Eccentricity 0.251 0.641
Inclination 13.11° 7.04°
Spin period 5.385 h 12.761 h
Mean radius 62 km 2.2 km
Magnitude 7.30 11.30
Discovery 1880 1969

The irregular shapes of these two bodies make them interesting targets for a study addressing the gravitation of any object. Let us see now how the authors addressed the problem.

Numerical modeling

Several models exist in the literature to address the gravity field of planetary bodies. The first approximation is to consider them as spheres, then you can refine in seeing them as triaxial ellipsoids. For highly irregular bodies you can try to model them as cuboids, and then as polyhedrons. Another way is to see them as duplexes, this allows to consider the inhomogeneities dues to the two masses constituting bilobate objects. The existence of previous studies allow a validation of the model proposed by the authors.

And their model is a finite-element numerical modeling. The idea is to split the surface of the asteroid into small triangular planar facets, which should be very close to the actual surface. The model is all the more accurate with many small facets, but this has the drawback of a longer computation time. The facets delimit the volume over which the equations are integrated, these equations giving the local self-gravitational and the impact disruption energies. The authors also introduce the energy rebate, which is a residual energy, due to the fact that you can remove material without removing half of it. This means that the impact disruption energy, as it is defined in the literature, is probably a too strong condition to have extrusion of material.
The useful physical quantities, which are the gravitational potential, the attraction, and the surface slope, are propagated all along the body thanks to a numerical scheme, which accuracy is characterized by an order. This order quantifies the numerical approximation which is made at each integration step. A higher order is more accurate, but is computationally more expensive.

Once the code has been run on test cases, the authors applied it on Kleopatra and Churyumov-Gerasimenko, for which the shape is pretty well known. They used meshes of 4,094 and 5,786 faces, respectively.

Results

The validation phase is successful. The authors show that with a 3rd order numerical scheme, they recover the results present in the literature for the test cases with an accuracy of ~0.1%, which is much better than the accuracy of the shape models for the real asteroids. Regarding Kleopatra and Churyumov-Gerasimenko, they get the gravity field at any location, showing in particular excesses of gravity at the two lobes.

Such a study is particularly interesting for further missions, which would determine the gravity field of asteroids, which would then be compared with the theoretical determination by this code. Other applications are envisaged, the authors mentioning asteroid mining.

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 and Facebook.

And Merry Christmas!