Tag Archives: Rotation

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.

Rotational stability of Ceres and Vesta

Hi there! The question we address today is: how stable are the rotations of Ceres and Vesta? Do you remember these two guys? These are the largest two asteroids in the Main Belt, and the spacecraft Dawn visited them recently. It gave us invaluable information, like the maps of these bodies, their shapes, their gravity fields, their rotational states…
The study I present you today, Long-term orbital and rotational motions of Ceres and Vesta, by T. Vaillant, J. Laskar, N. Rambaux, and M. Gastineau, wonders how permanent the observed rotational state is. This French study has recently been accepted for publication by Astronomy & Astrophysics.

Ceres and Vesta

I already told you about these two bodies. (1)Ceres (“(1)” because it was the first asteroid to be discovered) is known since January 1801. It has been discovered by the Italian astronomer Giuseppe Piazzi at Palermo Astronomical Observatory. The spacecraft Dawn orbits it since April 2015, but is now inoperative since November 1st, 2018. We see Ceres as a body with a rocky core and an icy mantle, possibly with an internal ocean.

Before visiting Ceres, Dawn orbited Vesta, between July 2011 and September 2012. (4)Vesta has been discovered 6 years after Ceres, in 1807, by the German astronomer Heinrich Olbers. This is a differentiated body, probably made of a metallic core, a rocky mantle, and a crust. It has been heavily bombarded, showing in particular two large craters, Rheasilvia and Veneneia. Vesta is the source of the HED (Howardite Eucrite Diogenite) meteorites, which study is an invaluable source of information on Vesta (see here).

The surface of Vesta (detail). © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
The surface of Vesta (detail). © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA

You can find below some numbers regarding Ceres and Vesta.

(1) Ceres (4) Vesta
Discovery 1801 1807
Semimajor axis 2.77 AU 2.36 AU
Eccentricity 0.116 0.099
Inclination 9.65° 6.39°
Orbital period 4.604 yr 3.629 yr
Spin period 9.07 h 5.34 h
Obliquity 4.00° 27.47°
Shape (965.2 × 961.2 × 891.2) km (572.6 × 557.2 × 446.4) km
Density 2.08 g/cm3 3.47 g/cm3

As you can see, Vesta is the closest one. It is also the most elongated of these bodies, i.e. you definitely cannot consider it as spherical. Both have significant orbital eccentricities, which means significant variations of the distance to the Sun (this will be important, wait a little). You can also see that these are fast rotators, i.e. they spin in a few hours, while their revolution periods around the Sun are of the order of 4 years. By the way, Vesta rotates twice faster than Ceres. Such numbers are pretty classical for asteroids.
You can also notice that Vesta is denser than Ceres, which is consistent with a metallic core.
Finally, the obliquities. The obliquity is the angle between the angular momentum (somehow the rotation axis… this is not exactly the same, but not too far) and the normal to the Sun. In other words, a null obliquity means that the body rotates along its orbit. An obliquity of 90° means that the body rolls on its orbit. An obliquity of 180° means that the body rotates along its orbit… but its rotation is retrograde (while it is prograde with a null obliquity).
Here, you can see that the obliquity of Ceres is close to 0, while the one of Vesta is 27°, which is significant. It is actually close to the obliquity of the Earth, this induces yearly variations of the insolation, and the seasons. On bodies like Ceres and Vesta, the obliquity would affect the survival of ice in deep craters, i.e. if the obliquity and the size of the crater prevents the Sun to illuminate it, then it would survive as ice.
From these data, the authors simulated the rotational motion of Ceres and Vesta.

Simulating their rotation

Simulating the rotation consists in predicting the time variations of the angles, which represent the rotational state of the bodies. For that, you must start from the initial conditions (what is the current rotational state?), and the physical equations, which rule the rotational motion.
For rigid bodies, rotation is essentially ruled by gravity. The gravitational perturbation of the Sun (mostly) and the planets affects the rotation. You quantify this perturbation with the masses of the perturbers, and the distances between your bodies (Ceres and Vesta), and these perturbers. To make things simple, just take Ceres and the Sun. You know the Solar perturbation on Ceres from the mass of the Sun, and the orbit of Ceres around it. This is where the eccentricity intervenes. Once you have the perturbation, you also need to determine the response of Ceres, and you have it from its shape. Since Vesta is more triaxial than Ceres, then its sensitivity to a gravitational should be stronger. It mostly is, but you may have some resonances (see later), which would enhance the rotational response.

The rotational stability

The question of the rotational stability is: you know, the numbers I gave you on the rotation… how much would they vary over the ages? This is an interesting question, if you want to know the variations of temperature on the surface. Would the ice survive? Would the surface melt? Would that create an atmosphere? For how long? Etc.
For instance, the same team showed that the obliquity of the Earth is very stable, and we owe it to our Moon, which stabilized the rotation axis of the Earth. This is probably a condition for the habitability of a telluric planet.

Let us go back to Ceres and Vesta. The authors focused on the obliquity, not on the spin period. In fact, they considered that the body rotated so fast, that the spin period would not have any significant effect. This permitted them to average the equations over the spin period, and resulted in a rotational dynamics, which moves much slower. And this allows to simulate it over a much longer time span.

A symplectic integrator for a long-term study

A numerical integration of the equations of the rotational motion, even averaged over the fast angle (I mean, the rotation period), may suffer from numerical problems over time. If you propagate the dynamics over millions of years, then the resulting dynamics may diverge significantly from the real one, because of an accumulation of numerical errors all along the process of propagation.

For that, use symplectic integrators. These are numerical schemes, which preserve the global energy of the dynamics, if you have no dissipation of course. But there are many problems of planetary dynamics, which permit you to neglect the dissipation.

When you can neglect the dissipation, your system is conservative. In that case, you can use the mathematical properties of the Hamiltonian systems, which preserve the total energy. That way, your solution does not diverge.

But how to determine whether your dynamics is stable or not? There are many tools for that (Lyapunov exponents, alignment indexes…) Here, the authors determined the diffusion of the fundamental frequencies of the system.

Diffusion of the fundamental frequencies

Imagine you orbit around the Sun, at a given period… actually the period depends on your semimajor axis, so, if it remains constant, then the orbital period remains constant. If your orbit is also disturbed by another perturber, you will see periodic variations in your orbital elements, which correspond to the period of the perturber. Very well. So, analyzing the frequencies which are present in your motion should give you constant numbers…

But what happens if your bodies drift? Then your frequencies will drift as well. In detecting these variations, which result from the so-called diffusion of the fundamental frequencies of the system, you detect some chaos in the system. I took the example of the orbital dynamics, but the same works for the rotation. For instance, the orbital frequencies appear in the time evolution of the rotational variables, since the orbit affects the rotation. But you also have proper frequencies of the rotational motion, for instance the period at which the angular momentum precesses around the normale to the orbit, and this period may drift as well…

The diffusion of the fundamental frequencies is one indicator of the stability. The authors also checked the variations of the obliquity of Ceres and Vesta, along their trajectories. They simulated the motion over 40 Myr (million years), in considering different possible numbers for the interior, and different initial obliquities.

Let us see now the results.

Obliquity variations up to 20 degrees

If you consider different possibilities, i.e. we do not know how these bodies were 40 Myr ago, then we see that it is theoretically possible for them to have been highly influenced by a resonance. This means that one fundamental frequency of the rotation would have been commensurable with periodic contributions of the orbital motion, and this would have resulted in a high response of the obliquity. For the present trajectories, the author estimate that the obliquity of Ceres could have varied between 2 and 20° these last 20 Myr, and the obliquity of Vesta between 21 and 45°.

To be honest, this is only a part of a huge study, which also investigates the stability of the orbital motions of Ceres and Vesta. Actually, these bodies are on chaotic orbits. This does not mean that they will be ejected one day, but that their orbits becomes uncertain, or inaccurate, after some tens of Myr.

The study and its authors

  • You can find the study here. The authors made it also freely available on arXiv, many thanks to them for sharing! And now the authors
  • Unfortunately I did not find any webpage for the first author Timothée Vaillant. You can find here the one of Jacques Laskar, second author of the study,
  • and the IAU page of Mickaël Gastineau.

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.

What if the Earth rotated backwards?

Hi there! I recently realized that over more than 100 articles, I never spoke about our Earth. Of course, you can say that, when I mean planets, I implicitly mean planets other than our Earth… There was probably something like that…
Anyway, our Earth is our home, and as such, it is of the uttermost importance. In particular, the global warming threatens it, and threatens the mankind itself. This is why we must study the Earth, but don’t worry, the Earth is studied.
Today I present simulations of the climate that the Earth would have, if it rotated backwards, at the same rate.
Of course, this is a theoretical study, which does not reproduce a real situation. But this is anyway interesting, because it permits us to understand the role of the different factors, which affect the climate. What is the role of the spin direction?
This is the question this study answers. The study is The climate of a retrograde rotating Earth, by Uwe Mikolajewicz et al., and it has recently been published in Earth System Dynamics.

The climate of our Earth

The climate of our Earth is influences by 4 factors:

  1. the astronomical factors
  2. the atmospheric circulation
  3. the oceanic circulation
  4. the ones I forget

The astronomical factors (axial tilt)

The obliquity of the Earth, or axial tilt, is responsible for the seasons. The rotation axis of our Earth is not orthogonal to its orbital plane around the Sun (the ecliptic), but is tilted by some 23° (somehow the angle between your index and your middle fingers, when you open your hand). The consequence is that the two poles do not see the sunlight six months a year, alternatively. And the other regions of the Earth have varying day durations, which affect the temperature. You have the seasons.

The team of Jacques Laskar (IMCCE, Paris Observatory) has shown that the Moon stabilizes the axial tilt of the Earth (see here). In other words, a moonless Earth would have experienced large variations of the axial tilt, hence large variations of the climate. So large that they may have threatened the development of life on Earth, since we need to adapt to the climate. We can do it when the changes are slow enough… and our fear with global warming is not (only) the warming itself, but its acceleration… Anyway, we are alive thanks to our Moon.

In fact, the astronomic forcing affects the climate on a wider range. The Serbian geophysicist and astronomer Milutin Milanković has hypothesized (and this has been confirmed by several teams since then) that the variations of the orbit and the rotation of the Earth were responsible for the paleoclimates. This theory is now known as the Milanković cycles.

But astronomic forcing is not everything. This affects the insolation of a given place, providing some energy to heat the Earth (not the whole energy actually, but let us neglect this point). Once a planet is illuminated, it responds… and the response depends on its constituents, the atmosphere playing a critical role.

The atmospheric circulation

As you know, our Earth is surrounded by an atmosphere, which is a layer of air, mostly composed of nitrogen and oxygen. Its pressure decreases with the altitude, 3 quarters of it being in the 11 lowest kilometers, while the boundary at the atmosphere is considered to be at about 100 km. This atmosphere is responsible for greenhouse effect, which heats the surface. It also increases the pressure, this permits the existence of liquid water. Moreover, it protects us from ultraviolet radiation, meteorites (many of them being fragmented when encountering the atmosphere), and allows us to breath. You can forget life on an atmosphereless Earth.

Beside this, the atmospheric circulation redistributes the thermal energy on Earth. You know the winds.
More precisely, this circulation is structured as cells, which take hot air at given locations of the surface, before releasing it back somewhere else. The main effect is due to latitudinal cells (Hadley, Ferrel, and polar cells), which permit heat transfers between different latitudes, but there is also a longitudinal motion, known as zonal overturning circulation.

Oceans play a key role in the regulation of our climate, since they have a kind of thermal inertia, which affects the temperature of the coastal areas.

The oceanic circulation

I mean the oceanic currents, which are water displacements. This may transfer hot water to colder regions, and conversely. An example is the North Atlantic Drift, aka Gulf Stream, which is responsible for the pretty moderate winters in Europe, while Canada freezes. There are also currents designated as gyres, since they have a pretty circular motion on a very large scale.
Moreover, you also have formation of water masses in the Atlantic, i.e. masses of water, which properties (temperature, salinity,…) are pretty homogeneous, and different from the surrounding waters.

Atmospheric and oceanic circulations are influence by the Coriolis effect, which is the consequence of the Earth rotation… and this study is on the influence of the Earth rotation.

The ones I forget

Sorry, I don’t remember 🙂

Let me mention anyway the influence of the land, which of course blocks the oceanic currents, and also may affect the atmospheric ones, in particular if you have mountains.

Different climates

All of these effects make meteorology a very complicated science. And you also have different climates on Earth, such as (following Köppen climate classification):

  • tropical climates (constant high temperatures),
  • dry climates (deserts),
  • temperate climates,
  • continental climates, where you have large variations of temperature between summer and winter,
  • and polar climates (the coldest ones).

You cannot pretend simulating the climate of the Earth if you don’t get these 5 climates.

The Max Planck Institute Earth System Model

The authors are experts in climate simulation. This is a very difficult task, since you have to implement the interactions between all the physical parameters (insolation, oceanic currents, atmospheric circulation,…), in a code which is non-linear and depends on multiple variables. Basically, when an equation is non-linear, you cannot simply derive its solution. Instead, you need to integrate the equation numerically, and the solution may be very sensitive to your parameters, your initial conditions (how is the climate when you start the simulations?), and your numerical scheme.

In particular, you split the atmosphere and the oceans on a grid of finite elements, and your numerical code simulates the solution element by element, time after time. This requires high performance computing tools.

The authors dispose of a dedicated numerical model, the Max Planck Institute Earth System Model (MPI-ESM), which couples the atmosphere, ocean and land surface through the exchange of energy, momentum, water and carbon dioxide. This homemade tool has been developed after years of study. It interfaces the simulations of different physical processes, all of them having been developed and improved since many years.
The authors have used the MPI-ESM many times in the past, which makes it reliable.

Intensive numerical simulations

In present study, the authors ran two sets of simulations:

  • CNTRL, which are consistent with our knowledge of the Earth,
  • and RETRO. To each CNTRL simulation corresponds a RETRO one, in which the Earth rotates backwards.

Each set is composed of 1,850 climate conditions (i.e. 1,850 different simulations), over 6,990 years. The authors point out that the simulations should be over a long enough duration, to permit the climate to reach an equilibrium state. The simulations show that in practice, the equilibrium is reached in some 2,000 years.

CNTRL simulations are necessary since, if you just compare a RETRO simulation with our observed climate, you cannot be sure whether the difference comes from the retrograde rotation, or from an effect which would have been inaccurately modeled. Moreover, running so many simulations permits to distinguish robust solutions, which give in some sense the same climate for many simulations, from anecdotic ones, i.e. due to particular initial conditions. Such a non-linear system of equations (Navier-Stokes, etc.) may be chaotic, which implies to be possibly very sensitive to the initial conditions, in a given range which we do not really know…

In the RETRO simulations, the backward rotation is modeled as:

  • the inversion of the Coriolis parameter in the oceanic and atmospheric circulations,
  • the inversion of the Sun’s diurnal march in the calculations of radiative transfer.

And one the simulations have run, they get the results. The question you may ask is: would that affect the global temperature of the Earth? It appears that no. You have no change on average, I mean the mean temperature remains pretty the same, but you have dramatic local changes. Let me emphasize two of them.

The Atlantic and the Pacific exchange their roles

As you can imagine, the inversion of the rotation results in inversion of the oceanic currents and the zonal winds. No need to run the simulations to predict this. But the simulations show unexpected things.

The Atlantic ocean is known for its water masses, and the CNTRL simulations get them. However, the RETRO simulations do not have them in the Atlantic, but in the Pacific Ocean.

A green Sahara

Another change is that the monsoons occur in the Sahara and Arabian Peninsula. This dry area, made of desert, would be a forest if the Earth rotated backwards! However, the world’s biggest desert would have been in the Southern Brazil and Argentina.

You can finally ask: why the authors did this study, since a backward rotating Earth is not realistic? Just because we need to fully understand the climate, and the rotation direction is one of the effects affecting it. We do not know whether this could apply to an extrasolar planet, or whether the results would help us to understand something else… That’s research, but trust me, it is useful one! Climate science has become a critical topic.

The study and its authors

And now, the 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

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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.

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