Tag Archives: Rotation

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

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 rotation of ‘Oumuamua

Hi there! Today we go back to ‘Oumuamua, you know, this interstellar object discovered last Fall. Its visit to our Solar system was the opportunity to observe it, and here we discuss on an analysis of the variations of its luminosity. I present you The excited spin state of 1I/2017 U1 ‘Oumuamua, by Michael J.S. Belton and collaborators. This study tells us that its rotation state might be complex, and that affects the way we figure out its shape. It has recently been published in The Astrophysical Journal Letters.

Remember 1I/’Oumuamua?

I already told you about ‘Oumuamua. This is the first identified object, which has been found in our Solar System but which undoubtedly originates from another System. In other words, it was formed around another star.
The Pan-STARRS survey identified ‘Oumuamua in October 2017, and the determination of its orbit proved it to be unusually eccentric. With an eccentricity close to 1.2, its orbit is a branch of a hyperbola rather than an ellipse. This means that it comes from very far, passes by while the Sun deviates it, and leaves us for ever.
This is the highest eccentricity ever recorded in the Solar System so far. Other objects had an eccentricity larger than 1, but which could have been caused by the gravitational perturbation of a planet. Not for ‘Oumuamua.
Its full name is actually 1I/2017 U1 (ʻOumuamua). 2017 because it was discovered in 2017, 1I as the first Interstellar object ever discovered (by the way, the International Astronomical Union has created this category for ‘Oumuamua), and the name ‘Oumuamua means scout in Hawaiian.

The announcement of its discovery motivated the observers all around the world to try to observe it and make photometric measurements. Here we discuss what these measurements tell us on the rotation and the shape. But before that, let me tell you something on the rotation.

Different modes of rotation

We will consider that our object is an ellipsoid. This is actually unsure, but let us assume it. We have 3 different axes, and we could imagine different configurations for its rotation:

  1. Tumbling rotation: the object rotates around its 3 axes, and basically this is a mess. We could be in a situation of dynamical chaos, like for the moon of Saturn Hyperion.
  2. Short-axis mode (SAM): the rotation is strongly dominated by a motion around the shortest axis. This is the case for many bodies in the Solar System, like the planets, our Moon… This does not mean that the rotation is strictly around one axis, but we will see that a little later.
  3. Long-axis mode (LAM): the rotation is strongly dominated by a motion around the longest axis.
The LAM and SAM modes.
The LAM and SAM modes.

These last two modes can actually cohabit with tumbling, i.e. a tumbling rotation may favor rotation around one axis.

If the rotation were strictly around one axis, then the body would look like a top. But this rotation axis may move with respect to the figure axis. This motion is named precession-nutation. The precession is the averaged path of the figure axis around the angular momentum, while the nutation contains the oscillations around it.

Now, imagine that you look at an object, which has such a rotation. How can you estimate it? There are ways.

Observing the rotation

Actually the brightness of a body not only depends on the distance from it, or on the insolation angle, but also on the surface facing you. This means that from the brightness, you can deduce something on the rotation state of the object. In particular, this surface brightness depends on its location with respect to the principal axis. If the object has the shape of a cigar, the reflected light from the long axis and from the short one will be different, and the lightcurve will present periodic variations. And the period of these variations is the rotation period. Easy, isn’t it?

Actually, not that easy. First, you assume that the surface has a constant albedo, i.e. that the ratio between the incident and the reflected lights is constant. But you do not know that. In particular, an icy surface has a higher albedo than a carbonaceous one. Another difficulty: a tumbling object, or even one with a precessional component in its rotation, will present a combination of different frequencies. Of course, this complicates the analysis.

However, you simplify the analysis in adding observations to your dataset. The authors used 818 observations over almost one month, spanning from Oct, 25 to Nov, 23, 2017. This includes observations from the Hubble Space Telescope, from the Magellan-Baade telescope at Las Campanas Observatory (Chile), from the Canada-France-Hawaii Telescope, from Pan-NSTARRS (these last facilities being based in Hawaii)…

Once the observations are obtained as raw data, they must be treated to correct from atmospheric and instrumental problems. And then it is not done yet, since the authors need an absolute luminosity of ‘Oumuamua, i.e. as if its distance to the observer were constant. The motion of ‘Oumuamua actually induced a trend in its distance to the Earth, and a trend in its luminosity, which the authors fitted before subtracting it the measured lightflux.

Once this is done, the authors get a lightcurve, which is constant on average, but presents variations around its mean value. Unfortunately, the required treatment induced an uncertainty in the measurements, which the authors had to consider. But fortunately, these practical difficulties are well-known, and algorithms exist to extract information from such data.

2 numerical algorithms

Basically, you need to extract periods from the variations of the lightflux. For that, we dispose of the classical tool of Fourier Transforms, which in principle requires equally spaced data. But the recorded data are not equally spaced, and remember that you must consider the uncertainties as well.

Specific algorithms exist for such a purpose. The authors used CLEAN and ANOVA, to double-check their results. These algorithms allow in particular to remove the aliasing effect, i.e. a wrong measurement of a period, because of an appropriate spacing of the data. And now, the results!

A cigar or a pancake?

The authors found two fundamental periods in the lightcurves, which are 8.67±0.34 and 3.74±0.11 hours. Interestingly, they connected these measurements to the possible dynamics of rotation, and they found two possible solutions:

  1. Long-Axis Mode: In that case, the possible rotation periods are 6.58, 13.15 and 54.48 hours, the latter being the most probable one.
  2. Short-Axis Mode: Here, ‘Oumuamua would be rotating with respect to the short-axis, but also with oscillations around the long axis of periods 13.15 or 54.48 hours.

In both axis, the long axis would also precess around the angular momentum in 8.67 ± 0.34 hours. Moreover, the authors found constraints on its shape. Previous studies already told us that ‘Oumuamua is highly elongated, this study confirms this fact, and tells us that ‘Oumuamua could be somewhere between the cigar and the pancake. But once more, this result could be weakened by variations of the surface albedo of ‘Oumuamua.

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.

2010 JO179: a new, resonant dwarf planet

Hi there! Today I present you the discovery of a Trans-Neptunian Object, you know, these objects which orbit beyond the orbit of Neptune. And I particularly like that one, since its orbit resonates with the one of Neptune. Don’t worry, I will explain you all this, keep in mind for now that this object is probably one of the most stable. Anyway, this is the opportunity to present you A dwarf planet class object in the 21: 5 resonance with Neptune by M.J. Holman and collaborators. This study has recently been accepted for publication in The Astrophysical Journal Letters.

The Trans-Neptunian Objects

The Trans-Neptunians Objects are small bodies, which orbit beyond the orbit of Neptune, i.e. with a semimajor axis larger than 30 AU. The first discovered one is the well-known Pluto, in 1930. It was then, and until 2006, considered as the ninth planet of the Solar System. It was the only known TNO until 1992. While I am writing this, 2482 are listed on the JPL small-body database search engine.

The TNOs are often classified as the Kuiper-Belt objects, the scattered disc objects, and the Oort cloud. I do not feel these are official classifications, and there are sometimes inconsistencies between the different sources. Basically, the Kuiper-Belt objects are the ones, which orbits are not too much eccentric, not too inclined, and not too far (even if these objects orbit very far from us). The scattered disc objects have more eccentric and inclined orbits, and these dynamics could be due to chaotic / resonant excitation by the gravitational action of the planets. And the Oort cloud could be seen as the frontier of our Solar System. It is a theoretical cloud located between 50,000 and 200,000 Astronomical Units. Comets may originate from there. Its location makes it sensitive to the action of other stars, and to the Galactic tide, i.e. the deformation of our Galaxy.

The object I present you today, 2010 JO179, could be a scattered disc object. It has been discovered in 2010, thanks to the Pan-STARRS survey.

The Pan-STARRS survey

Pan-STARRS, for Panoramic Survey Telescope and Rapid Response System, is a systematic survey of the sky. Its facilities are located at Haleakala Observatory, Hawaii, and currently consist of two 1.8m-Ritchey–Chrétien telescopes. It operates since 2010, and discovered small Solar System objects, the interstellar visitor 1I/’Oumuamua… It observes in 5 wavelengths from infrared to visible.

The Pan-STARRS1 telescope. © Pan-STARRS
The Pan-STARRS1 telescope. © Pan-STARRS

The data consist of high-accuracy images of the sky, containing a huge amount of data. Beyond discoveries, these data permit an accurate astrometry of the object present on the images, which is useful for understanding their motion and determining their orbits. They also allow a determination of the activity of variable objects, i.e. variable stars, a study of their surface from their spectrum in the five wavelengths, and (for instance) the measurement of their rotation. A very nice tool anyway!

Pan-STARRS delivered its first data release in December 2016, while the DR2 (Data Release 2) is scheduled for mid-2018… pretty soon actually.

Among the discovered objects are the one we are interested in today, i.e. 2010 JO179.

Identifying the new object

The first observation of 2010 JO179 dates back from May 2010, and it has been detected 24 times during 12 nights, until July 2016. The detections are made in comparing the Pan-STARRS data from the known objects. Once something unknown appears in the data, leaving what the authors call a tracklet, its motion is extrapolated to predict its position at different dates, to investigate whether it is present on other images, another time. From 3 detections, the algorithm makes a more systematic search of additional tracklets, and in case of positive additional detection, then an orbit is fitted. The orbital characteristics (and other properties) are listed below.

Semimajor axis 78.307±0.009 AU
Eccentricity 0.49781±0.00005
Inclination 32.04342±0.00001 °
Orbital period 6663.757±0.002 yr
Diameter 600-900 km
Absolute magnitude 3.4±0.1

You can notice the high accuracy of the orbital parameters, which almost looks like a miracle for such a distant object. This is due to the number of detections, and the accuracy of the astrometry with Pan-STARRS. Once an object is discovered, you know where it is, or at least where it is supposed to be. Thanks to this knowledge, it was possible to detect 2010 JO179 on data from the Sloan Digital Sky Survey, taken in New Mexico, and on data from the DECalS survey, taken in Chile. Moreover, 2010 JO179 was intentionally observed with the New Technology Telescope (NTT) in La Silla, Chile.

The spectroscopy (analysis of the reflected light at different wavelengths) of 2010 JO179 revealed a moderately red object, which is common for TNOs.

Measuring its rotation

This is something I have already evoked in previous articles. When you record the light flux reflected by the surface of a planetary body, you should observe some periodic variability, which is linked to its rotation. From the observations, you should extract (or try to) a period, which may not be an easy task regarding the sparsity and the accuracy of the observations.

In using the so-called Lomb-Scargle algorithm, the authors detected two possible periods, which are 30.6324 hours, and 61.2649 hours… i.e. twice the former number. These are best-fits, i.e. you try to fit a sinusoid to the recorded light, and these are the periods you get. The associated amplitudes are variations of magnitude of 0.46 and 0.5, respectively. In other words, the authors have two solutions, they favor the first one since it would imply a too elongated asteroid. Anyway, you can say that twice 30.6324 hours is a period as well, but what we call the spin period is the smallest non-null duration, which leaves the light flux (pretty) invariant. So, the measured spin period of 2010 JO179 is 30.6324 hours, which makes it a slow rotator.

Mean-motion resonances

Let us make a break on the specific case of 2010 JO179 (shall we give it a nickname anyway?), since I would like to recall you something on the mean-motion resonances before.

When two planetary bodies orbit the Sun, they perturb each other. It can be shown that when the ratio of their orbital periods (similarly the ratio of their orbital frequencies) is rational, i.e. is one integer divided by another one, then you are in a dynamical situation of commensurability, or quasi-resonance. A well known case is the 5:2 configuration between Jupiter and Saturn, i.e. Jupiter makes 5 orbits around the Sun while Saturn makes 2. In such a case, the orbital perturbations are enhanced, and you can either be very stable, or have a chaotic orbit, in which the eccentricities and inclinations could raise, the orbit become unpredictable beyond a certain time horizon (Lyapunov time), and even a body be ejected.

Mathematically, an expansion of the so-called perturbing function, or the perturbing mutual gravitational potential, would display a sum of sinusoidal term containing resonant arguments, which would have long-term effects. These arguments would read as pλ1-(p+q)λ2+q1ϖ1+q2ϖ2+q3Ω1+q4Ω2, with q=q1+q2+q3+q4. The subscripts 1 and 2 are for the two bodies (in our case, 1 will stand for Neptune, and 2 for JO 2010179), λ are their mean longitudes, ϖ their longitudes of pericentres, and Ω the longitudes of their ascending nodes.

In a perturbed case, which may happen for high eccentricities and inclinations, resonances involving several arguments may overlap, and induce a chaotic dynamics that could be stable… or not. You need to simulate the long-term dynamics to know more about that.

A resonant long-term dynamics

It appears that Neptune and 2010 JO179 are very close to the 21:5 mean-motion resonance (p=5, q=16). To inquire this, the authors ran 100 numerical simulations of the orbital motion of 2010 JO179, with slightly different initial conditions which are consistent with the uncertainty of the observations, over 700 Myr. And they saw that 2010 JO179 could be trapped in a resonance, with argument 5λ1-21λ2+16ϖ2. In about 25% of the simulations, JO179 remains trapped, which implies that the resonant argument is librating, i.e. bounded, all over the simulation. As a consequence, this suggests that its orbit is very stable, which is remarkable given its very high eccentricity (almost 0.5).

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.