Category Archives: Comets

The rotation of 67P/Churyumov-Gerasimenko

Hi there! Today, we go back to the famous comet 67P / Churyumov-Gerasimenko. As you may know, this comet was the target of the European space mission Rosetta. In particular, it was the first comet to be landed by a spacecraft, in November 2014. Rosetta gave us invaluable information on 67P, which could be extrapolated to many comets, with caution of course. Today we discuss Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation induced torques, by T. Kramer, M. Läuter, S. Hviid, L. Jorda, H.U. Keller and E. Kührt.
It addresses the following issue: when you try to assess the forces affecting the orbit and the rotation of the comet, you have troubles. Among these forces are the gravitational perturbations of the Sun and the planets, which are very well known, but also torques and forces due to non-gravitational effects. When the comet approaches the Sun, its ice sublimates, and the resulting outgassing deviates the comet and affects its rotation. This last effect is only poorly constrained, and this is why in situ observations, as made by Rosetta, are essential to understand them. This study has recently been accepted for publication in Astronomy and Astrophysics.

The discovery of 67P / Churyumov-Gerasimenko

This comet has been discovered by chance in September 1969 at Alma Ata Observatory, now in Kazakhstan, then in USSR. Svetlana Ivanova Gerasimenko took images of a field containing the comet 32P/Comas Solá, and Klim Ivanovich Churyumov detected there a new object close to the edge of an image. This object appeared on several images, which permitted to characterize its motion. That object was itself a comet, a periodic one (“P”), and more precisely the 67th to be discovered. So was it named 67P / Churyumov-Gerasimenko. You can find below some of its characteristics.

Discovery 1969
Semimajor axis 3.463 AU
Perihelion 1.243 AU
Aphelion 5.68 AU
Eccentricity 0.64
Inclination 7.04°
Orbital period 6.44 yr
Spin period 12 h 24 min
Diameter 4 km
Density 0.53 g/cm3

As you can see, its orbit is pretty elongated, and has a period of almost 6.5 years. This means that every 6.5 years, 67P/Churyumov-Gerasimenko approaches the Sun, at its perihelion, and at that time gets heated. This results in the sublimation of some of its material, which deviates it and alters its spin. The last passage at the perihelion occurred in August 2015, while the next one will be in November 2021. Rosetta orbited the comet from 2014 to 2016, which encompassed the perihelion passage, allowing to observe and measure the peak and evolution of its cometary activity.

A rugged terrain

We will see later that modeling the rotation of a planetary object requires to know its shape. Fortunately for us, we know this shape very accurately, thanks to Rosetta. Unfortunately for the authors, 67P/Churyumov-Gerasimenko is far from a ball.

This is actually a bilobal object, i.e. roughly like a bone, of some 4 km in its larger dimension. Moreover, its terrain is very rugged. Rosetta actually observed, over only two years, alterations in the terrain, e.g. a landslide associated with an outburst. This makes the behavior of the comet all the more difficult to constrain… For instance, if you want to consider an outburst, from which region will it emerge?

Rugged terrain on 67P © ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA
Rugged terrain on 67P © ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

The data brought by Rosetta

We know the shape and rotation state of 67P/Churyumov-Gerasimenko thanks to Rosetta/OSIRIS images. OSIRIS, for Optical, Spectroscopic, and Infrared Remote Imaging System, is an imager composed of 2 cameras, a WAC and a NAC (Wide-Angle and Narrow-Angle Camera, respectively). From images brought by OSIRIS, it was possible to build a set of approximately 25,000 control points. Multiple observations of these control points, at different dates, permitted to understand that

  • the comet spun around a single axis, which orientation has been determined,
  • its rotation period was 12 hours and something (on purpose, I do not detail this something here),
  • the rotation state varies with time. Rosetta observed a reorientation of the spin axis of 0.5°, and a shortening of the rotation period by 21 minutes (this is why I did not detail the something).

Moreover, these data permitted to elaborate a shape model of the comet, made of 3,996 triangular surface elements. From this shape model, you can determine what is called the tensor of inertia of the comet, i.e. its mass distribution, in assuming its composition to be homogeneous (you always have to make hypotheses).

Now, let us see how the rotation is affected.

The torques affecting the comet

In the study, the comet is assumed to be rigid, i.e. its shape is constant. You have no elasticity, this is probably a good approximation over such a limited time span. The equations of the rigid rotation tell you that the angular momentum of the comet (the angular momentum is the tensor of inertia, which is multiplied by the rotation) is affected by two kinds of torques:

  • the gravitational torque of the surrounding bodies, which is almost entirely due to the mass of the Sun,
  • non-gravitational torques, due to ice sublimation and heating by the Sun.

You put all this into an equation, you solve it numerically, and you can predict it, and understand the rotation measurements… Easy, isn’t it? Well, not that easy, since you have only few constraints on the ice sublimation.

Modeling its rotation

BUT you have measurements of the rotation. So, what you can do is fit the parameters you don’t know, to the observed rotation. And more particularly to the changes in the rotational state.

More precisely, the authors modeled the torque due to the sublimation of water ice with a Fourier representation, i.e. as a sum of periodic quantities. These contributions are assumed to have a period, which is due to the rotation of the comet, and they are treated separately. The authors managed to match the Fourier amplitudes with the observed torque. And now let us go to the conclusions.

What it tells us on the activity

Fitting the Fourier coefficients to the observed rotation finally tell us that:

  • you can constrain the active fraction of the surface, with respect to the different areas (the authors considered 38 different zones on the surface),
  • the sublimation increases much faster than linearly with respect to insolation. In other words, when you are twice closer to the Sun, the quantity of sublimated water ice is much more than twice than before. This was already known from other studies, but the study of the rotation confirms this fact. You should see it as a validation of the method.

So, this paper shows that we can definitely make a link between water production and the changes in rotation rate. Outgassing also produces CO2, but this is not considered, since this production is more uniform than the one of water, and so should not affect the reorientation of the spin axis.

The study and its authors

  • You can find the study here. The complete reference is Kramer T., Läuter M., Hviid S., Jorda L., Keller H.U. & Kührt E., 2019, Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation-induced torques, Astronomy and Astrophysics, in press. The authors made it also freely available on arXiv, many thanks to them for sharing! And now, let us see the authors:
  • the website of Tobias Kramer, first author of the study,
  • the webpage of Matthias Läuter,
  • the IAU page of Laurent Jorda,
  • the one of Horst Uwe Keller,
  • and the ResearchGate profile of Ekkehard Kührt.

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 Oort remembers

Hi there! You may know that in the Solar System, we have long period comets. These are comets which visit us, i.e. visit the vicinity of the Sun and the Earth, but on orbits which suggest that they will not come back before some centuries, maybe more. The Dutch astronomer Jan Oort hypothesized in 1950 that these comets originate from a hypothetical, I mean unobserved, cloud, which is now known as the Oort cloud. It is supposed to lie between 2,000 and 200,000 astronomical units (AU).
In the study we discuss today, The “memory” of the Oort cloud, by Marc Fouchard, Arika Higuchi, Takashi Ito and Lucie Maquet, the authors wonder how the original Oort cloud was like. For that, they investigate whether the present observations of the comets originating from it contain any information on its original shape. This study has recently been published in Astronomy and Astrophysics.

The Oort cloud

As I said, the Oort cloud as a reservoir for long-period comets had been suggested by Jan Oort in 1950. Actually, its existence had been hinted 18 years before, in 1932 by the Estonian astronomer Ernst Öpik, but he did not think that the small bodies constituting this cloud could eventually become observable comets, in the sense that they would have anyway orbited too far from the Sun, even at perihelion.

We now think that the Oort cloud consists of two parts: an inner and an outer cloud. The inner cloud would have the shape of a torus, limiting the inclination of its constituents. It would lie between 2,000 and 20,000 AU (remember: Neptune orbits at only 30 AU). However, the outer cloud, or isotropic cloud, would have a spherical distribution. It would lie between 20,000 and 50,000 AU, and be much less dense than the inner one.

The observable comets

The information we dispose of come from the orbits of observable comets. A comet is a small icy body, which presents a cometary activity, i.e. outgassing. This comes from the sublimation of the ice.
This activity is favored by the temperature, which is directly linked to the distance to the Sun. This is particularly striking for comets, which have significantly elongated (eccentric) orbits around the Sun. When an orbit is eccentric, you have significant variations of the distance between the Sun and the body, in other words, significant variations of the temperature, and consequently of the cometary activity.
Dynamically, a comet can be characterized by its orbital elements. The most interesting one is, in my opinion, the semimajor axis, which gives you the period (the time interval between two approaches of the comet to the Sun).
Some comets have periods smaller than 20 years, and are called Jupiter-family comets. From 20 to 200 years, you have the Halley-type comets (after the well-known comet 1P/Halley), and beyond that limit you have the long-period comets. These are the comets, which are of interest for us, i.e. they are supposed to originate from the Oort cloud.
In fact, there are comets which orbits are even longer than that… in the sense that these comets may never return. These are comets with very high orbital eccentricities (>0.99), they are almost parabolic… and some of them are even hyperbolic, i.e. they are not dynamically bound to the Sun. Those ones may come from an extrasolar system, but this is another story…

Anyway, we speak about the long-period comets. And the question is: what information do their orbits contain on the primordial Oort cloud?

Numerical simulations

To understand how this information is preserved, the authors ran simulations of the orbits of more than 200 million comets. These are fictitious comets, evolving under the influence of

  • planetary perturbations,
  • stellar passages,
  • the Galactic tide.

Planetary perturbations

Planetary perturbations are the gravitational actions of the four giant planets (Jupiter, Saturn, Uranus, and Neptune). They may have dramatic consequences in case of close encounter: the comet is such a small body with respect to a giant planet that it could have almost every orbit after the encounter. Some comets might even be destroyed (remember Shoemaker-Levy 9).

Stellar passages

These comets, initially in the proto-Oort cloud, orbit very far from the Sun. This means that they are only weakly dynamically bound to it, and potentially sensitive to perturbations from other stellar systems. In particular if one of them passes by. The authors considered this effect in adding random passing stars. The velocities of the stars measured by the astrometric satellite Gaia permit to constrain the most recent stellar passages, but far from all of them.

The Galactic tide

The Galactic tide is the deformation of our Milky Way under the gravitational influence of the other galaxies. Previous studies have shown that it has a significant influence on the Oort cloud. The gravitational force exerted by the Sun is there weak enough for the Galactic tide to be significant.

Galactic tide can actually be seen on images of galaxies, which are close enough. This results in galaxies with irregular shape.

Tidal interaction between two galaxies, seen by the Hubble Space Telescope.
Tidal interaction between two galaxies, seen by the Hubble Space Telescope.

Four classes of observable comets

Before presenting the way the authors addressed that question, I would like to mention that they considered 4 different sub-classes of these long-period, observable comets.

First, let us define an observable comet: an observable comet has a perihelion at less than 5 AU of the Sun. The perihelion is the point of the orbit, which is the closest to the Sun, and 5 AU roughly corresponds to the orbit of Jupiter. Among these observable comets, the authors called

  • jumpers the comets which perihelion was larger than 10 AU during the previous passage,
  • and creepers the other ones.

And among these jumpers and creepers, the authors identified the comets, prefixed KQ, which required the assistance of a close encounter with a giant planet (a planetary kick) to push them outward, making them then sensitive enough to the stellar passages and the galactic tide to be injected into the observable zone.
The letters K and Q come from the two guys who identified this phenomenon, i.e. Nathan Kaib and Thomas Quinn, in 2009.

So, the four classes of observable long-period comets that the authors distinguished are

  • the jumpers,
  • the KQ-jumpers,
  • the creepers,
  • the KQ-creepers.

The reason why they distinguished these four classes is that they have different behaviors. So, different outcomes regarding the dynamics may be expected.

Two models of cloud

So, the question is: when you start from a given proto-Oort cloud, how will the observable comets look like? I mean, how many of them will be observable? How will their perihelions be distributed? How inclined will they be?

And this depends (I should rather say: is assumed to depend) on the structure of your initial proto-Oort cloud. For that, the authors considered two models:

  • A disk-like distribution, in which the inclinations are limited to 20°,
  • an isotropic cloud, in which the comets may have any inclination. As such, it looks like the shell of an empty sphere.

And among these two models, the authors used several sets of initial conditions or their comets, in changing the distribution of orbital energy from one set to another.

Now, let us discuss the results.

The disk remembers

Unsurprisingly, the disc model results in 4 to 8 times more observable comets than the isotropic one. This should have been expected, since the giant planets have limited inclinations. So, you should have a limited inclination yourself to receive the assistance of a planet to become observable. Since it is not a sine qua non condition, you can have observable comets with high inclinations anyway, thanks to the Galactic tide and stellar passages.

Another outcome of the paper is that the KQ objects are preferably retrograde. This maximizes their odds to survive, i.e. not to be ejected from the Solar System, in being less sensitive to planetary perturbations. This is not an original result, since Kaib and Quinn already met this conclusion, but it always gives confidence to find a result, which was already known. It suggests that your study is right.

The new result is in the memory. The present study shows that, if you started from an isotropic disk, then stellar passages have wiped out its structure. However, the observable comets would keep from an initial disk (and here I quote the paper):

  • a concentration of comets along the ecliptic plane for semimajor axes smaller than 7,000 AU,
  • the typical wave structure of the Galactic tide.

Now, we should determine whether the initial Oort cloud was more like a disk, a more like a shell. This actually depends on the whole process of formation of the Solar System. Several scenarios compete, which means that we currently do not know. Anyway, this study suggests that counting the observable comets could give a clue on the nature of the original distribution (disk-like or shell-like), and if it is a disk, then we could be able to guess part of its structure.

The future can only bring us more information, thanks to the observational data of comets to be discovered.

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.

A blue comet

Hi there!

Today we discuss about the comet C/2016 R2. This comet has been discovered in September 2016, i.e. some 20 months before its closest approach to the Sun (passage at perihelion). Meanwhile, it heated more and more, and outgassed. This permitted many observations of the comet and its tails, and it appears that this comet is different from the classical ones. In what way? You have to read until the end.
I present The extraordinary composition of the blue comet C/2016 R2 (PanSTARRS), by N.Biver, D.Bockelée-Morvan, G.Paubert, R.Moreno, J.Crovisier, J.Boissier, E.Bertrand, H.Boussier, F.Kugel, A.McKay, N.Dello Russo and M.A.DiSanti. This study has recently been accepted for publication in Astronomy and Astrophysics.

The comet C/2016 R2

This comet has been discovered on September 7, 2016 at 6.3 astronomical units from the Sun, on the telescope Pan-STARRS (Panoramic Survey Telescope And Rapid Response System), which is located on the Haleakalā (Maui, Hawaii, USA). It was then moving toward its perihelion, i.e. toward the Sun. The passage occurred in May 2018, at a distance of 2.06 AU from the Sun. Since then, it is moving away, and it should come back in about 20,000 years… if it comes back. You can find below its orbital elements, taken from the JPL Small-Body Database Browser. These elements are computed from almost 3,000 observations, over 2 years (remember: the comet has been discovered in September 2016).

Semimajor axis 736.30 AU
Eccentricity 0.996
Inclination 58.22°
Perihelion distance 2.60 AU
Period 19,979.85 yr

This is what we call a long-period comets. You have comets of the Jupiter family, with period of a few years, you have comets with periods close to the century, like the very famous Halley comet, which period is 75 years (next passage in July 2061, be ready), and you have long-period comets like this one.

In fact, we have no proof that this comet already visited us 20,000 years ago, and we cannot be sure it will in 20,000 years. Look at the eccentricity: 0.996 is huge for an elliptic orbit, it actually means that the orbit is almost parabolic. In other words, it is close to never come back. Planetary perturbations or even a star passing by could be strong enough to destabilize the orbit of C/2016 R2, and make it leave our Solar System for ever. Conversely, it could make it more stable, and we can even imagine that this comet has an extrasolar origin. It could have been formed around another star, having been ejected from that system, having visited us, and been stabilized around the Sun. Which does not preclude a future ejection.
In fact, it is difficult to know, since such elongated orbits and such small objects are very sensitive to small planetary perturbations.

You can get clues on the origin of a planetary body by studying its composition. This may be pretty easy (or I should say: not that difficult) because

  1. amateurs are usually enthusiastic with comets,
  2. when a comet approaches the Sun, it creates beautiful tails.

When you observe the tails, you have part of the composition.

Spectroscopy of a comet

As discovered Fred Whipple, a comet is a dirty snowball, which is composed of a nucleus, and tails. This has been confirmed in 1986, when the comet 1P/Halley visited us. The nucleus is composed of water ice and silicates.

Approaching the Sun heats the comet, and sublimates its components. This is how it creates 3 tails:

  1. a dusty tail, which is the visible one. It is curved, and located behind the comet,
  2. an ion tail, which is made of gases. Its direction is opposite to the one of the Sun, because it is strongly affected by the Solar wind,
  3. a weak dusty antitail, which points opposite to the dust tail.

And for guessing the composition of these tails (you can also say the coma), you use spectroscopy. Basically:

  1. the Sun lights the tail,
  2. the Solar light is made of a wide spectrum of radiations. The radiations, which are characteristics of the elements present in the coma, are blocked.
  3. you observe the spectrum of the light crossing the coma. From this spectrum, you know which elements are present.

Of course, this is a little more complicated than that. First, you have to consider that the light you observe crosses the atmosphere, which affects it. So, you have to remove this effect. And then, you also have to consider that a cometary activity might be a weak process (depending on the perihelion distance and on the size of the nucleus), and some elements are sometimes observed, sometimes not. Fortunately, several teams have observed the comet, which secures the results.

For observing these spectra, you need dedicated facilities, which do not necessary observe the visible light. Let us present them now.

Many observation facilities

I here restrict to facilities used by the authors of that specific study, but there are many more.


IRAM is a French acronym for Institut de RAdioastronomie Millimétrique, or German for Institut für Radioastronomie im Millimeterbereich, or even Spanish for Instituto de Radioastronomía Milimétrica, i.e. institute of millimetric radioastronomy. What does that mean? It means that this facility observes in wavelengths, which are close to the millimeter. Remember that the visible light lies between 430 (for the red) and 700 (for the violet) nanometers, or 0.0007 millimeters. So, the human eye is definitely not sensitive to millimetric emissions. This part of the spectrum approaches the one of the radio waves.

IRAM is based in Grenoble, France, but Germany and Spain are also involved. Beside this, IRAM has worldwide collaborations.

It has 2 observing facilities:

  1. a 30 m radio telescope located on Pico Veleta (Andalucia, Spain),
  2. an interferometer, located on the Plateau de Bure, in the French Alps.

Both sites are at high altitude, i.e. 2,850 m for the Spanish site, and 2,550 m for the French one. IRAM has been created in 1979, and is still upgrading its facilities. Spain joined it in 1990, and the Plateau de Bure Interferometer, which was originally composed of 6 antennae, has now 10 and should have 12 by 2020, in the framework of the project NOEMA, for NOrthern Extended Millimeter Array. Its deployment, i.e. the inauguration of the seventh antenna, started in September 2014.

IRAM's 30m telescope at Pico Veleta © IRAM
IRAM’s 30m telescope at Pico Veleta © IRAM

The authors used the 30-m telescope based in Spain, to target the carbon monoxide, the hydrogen cyanide HCN, and the hydrogen sulfide H2S, at the frequencies 231, 266 and 169 GHz, respectively. The observations were conducted during two evenings, on 23 and 24 January 2018.


They also used the Nançay radio telescope. This facility is based in the center of France, and depends partly on Paris Observatory. The radio telescope observes centimetric waves. For that, it is composed of 2 mirrors, one is planar while the other one is spherical. These are mirrors for centimetric waves, i.e. these are actually railings, in which the metal bars are spaced by less than 1 centimeter. It mainly observes the wavelengths 21, 18 and 9 cm, which correspond to hydrogen, hydroxide OH, and the methylidyne radical CH.

The radio telescope, by <a href="//" title="User:Julien Descloux">Julien Descloux</a> — <span class="int-own-work" lang="fr">Travail personnel</span>, <a href="" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a>, <a href="">URL</a>
The radio telescope, by Julien DesclouxTravail personnel, CC BY-SA 3.0, URL

Beside this, Nançay has also a decametric interferometer composed of 144 antennae, and an antenna belonging to the Low-Frequency Array (LOFAR) network, which observes metric wavelengths.

The authors used the radio telescope between January and March 2018, for about one hour on average every 2 days.

Amateurs observations

These observations were supplemented by optical observations conducted by amateurs, who co-author the study.
The analysis of visible light could permit to detect, for instance, carbon monoxide CO (to confirm millimetric observations), the cyano radical CN, or the dinitrogen N2.

Detected species

First, the overall emission of the comet constrains the temperature of the gas. For C/2016 R2, it should be close to 23 K (-250°C, or -418°F).

Regarding the species: the authors detected a very large production of carbon monoxide CO. This, combined with a very low dust production (with respect to known comets), makes the coma to be blue, instead of tending to be red or yellow. And relatively to CO, there is a strong depletion of water H20, methanol CH3OH, formaldehyde H2CO, hydrogen cyanide HCN, and hydrogen sulfide H2S.

However, and this is very surprising, the authors detected an excess of dinitrogen N2, with a ratio N2/CO close to 0.08. In this case, N2 dominates the nitrogen budget.

Why so much dinitrogen

We don’t know! And this is why it is interesting.

Such an abundance of dinitrogen is very unusual. The only previous detection of dinitrogen was in situ, by Rosetta on 67P/Churyumov-Gerasimenko. In that case the ratio N2/CO was about 0.006, i.e. 10 times lower than for C/2016 R2. And for the other comets: just no detection.

This means that this comet did not form with the other comets. It formed elsewhere. And this makes this comet unique.

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.

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.