Tag Archives: asteroids

An interstellar asteroid

Hi there! You may have heard this week of our Solar System visited by an asteroid probably formed in another planetary system. This is why I have decided to speak about it, so this article will not be based on a peer-reviewed scientific publication, but on good science anyway. The name of this visitor is for now A/2017 U1.

History of the discovery

Discovering a new object usually consists in

  1. Taking a picture of a part of a sky. Usually these are parts of the order of the degree, maybe much less… so, small parts. And this also requires to treat the image, to correct for atmospheric (brightness of the sky, wind,…) and instrumental (dead pixels…) effects,
  2. Comparing in with the objects, which are known to be in that field.

If there is an unexpected object, then it could be a discovery. Here is the history of the discovery of A/2017 U1:

  • Oct. 19, 2017: Robert Weryk, a researcher of the University of Hawaii, discovers a new object while searching for Near-Earth Asteroids with the Pan-STARRS 1 telescope. An examination of images archives revealed that the object had already been photographed the day before.
  • Oct. 25, 2017: The Minor Planet Center (Circular MPEC 2017-U181) gives orbital elements for this new object, from 34 observations over 6 days, from Oct. 18 to 24. Surprisingly, an eccentricity bigger than 1 (1.1897018) is announced, which means that the trajectory follows a hyperbola. This means that if this object would be affected only by the Sun, then it would come from an infinite distance, and would leave us for infinity. In other words, this object would not be fated to remain in our Solar System. That day, the object was thought to be a comet, and named C/2017 U1. 10 observation sites were involved (once an object has been detected and located, it is easier to re-observe it, even with a smaller telescope).
  • Oct. 26, 2017: Update by the Minor Planet Center (Circular MPEC 2017-U185), using 47 observations from Oct. 14 on. The object is renamed A/2017 U1, i.e. from comet “C” to asteroid “A”, since no cometary activity has been detected. Same day: the press release announcing the first confirmed discovery of an interstellar object. New estimation of the eccentricity: e = 1.1937160.
  • Oct. 27, 2017: Update by the Minor Planet Center (Circular MPEC 2017-U234), using 68 observations. New estimation of the eccentricity: e = 1.1978499.

And this is our object! It has an absolute magnitude of 22.2 and a diameter probably smaller than 400 meters. These days, spectroscopic observations have revealed a red object, alike the KBOs (Kuiper Belt Objects). It approached our Earth as close as 15 millions km (0.1 astronomical unit), i.e. one tenth of the Sun-Earth distance.

The trajectory of A/2017 U1.
The trajectory of A/2017 U1.

What are these objects?

The existence of such objects is predicted since more than 40 years, in particular by Fred Whipple and Viktor Safronov. This is how they come to us:

  1. A protoplanetary disk creates a star, planets, and small objects,
  2. The small objects are very sensitive to the gravitational perturbations of the planets. As a consequence, they may be ejected from their planetary system, and become interstellar objects,
  3. They visit us.

Calculations indicate that A/2017 U1 comes roughly from the constellation Lyra, in which the star Vega is (only…) at 25 lightyears from our Sun. It is tempting to assume that A/2017 U1 was formed around Vega, but that would be only speculation, since many perturbations could have altered its trajectory. Several studies will undoubtedly address this problem within next year.

Maybe not the first one

Here we have an eccentricity, which is significantly larger (some 20%) than 1. Moreover, our object has a very inclined orbit, which means that we can neglect the perturbations of its orbit by the giant planets. In other words, it entered the Solar System on the trajectory we see now. But a Solar System object can get a hyperbolic orbit, and eventually be ejected. This means that when we detect an object with a very high eccentricity, like a long-period comet, it does not necessary mean that it is an interstellar object. In the past, some known objects have been proposed to be possible interstellar ones. This is for example the case for the comet C/2007 W1 (Boattini), which eccentricity is estimated to be 1.000191841611794±0.000041198 at the date May 26, 2008. It could be an IC (Interstellar Comet), but could also be an Oort cloud object, put on a hyperbolic orbit by the giant planets.

Detecting interstellar objects

A/2017 U1 object has been detected by the Pan-STARRS (for Panoramic Survey Telescope and Rapid Response System) 1 telescope, which is located at Haleakala Observatory, Hawaii. Pan-STARRS is constituted of two 1.8 m Ritchey–Chrétien telescopes, with a field-of-view of 3°. This is very large compared with classical instruments, and it is suitable for detection of bodies. It operates since 2010.

Detections could be expected from the future Large Synoptic Survey Telescope (LSST), which should operate from 2022 on. This facility will be a 8.4-meter telescope based in Chile, and will conduct surveys with a field-of-view of 3.5°. A recent study by Nathaniel Cook et al. suggests that LSST could detect between 0.001 and 10 interstellar comets during its nominal 10 year lifetime. Of course, 0.001 detection should be understood as the result of a formula. The authors give a range of 4 orders of magnitude in their estimation, which reflects how barely constrained the theoretical models are. This also means that we could be just lucky to have detected one.

What Pan-STARRS can do, LSST should be able to do. In a few years, i.e. in the late 2020s, the number or absence of new discoveries will tell us something on the efficiency of creation of interstellar objects in the nearby stars. Meanwhile, let us enjoy this exciting discovery!

The press release and its authors

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Equatorial cavities due to fissions

Hi there! Today I present you a theoretical study, which explains why some asteroids present cavities in their equatorial plane. The related paper, Equatorial cavities on asteroids, an evidence of fission events, by Simon Tardivel, Paul Sánchez & Daniel J. Scheeres, has recently been accepted for publication in Icarus.

When you see a cavity, i.e. a hole at the surface of a planetary, you… OK, I usually assume it is due to an impact. Here we have another explanation, which is that it spun so fast that it ejected some material. These cavities have been observed on the two NEOs (Near-Earth Objects) 2008 EV5 and 2000 DP107 α,for which the authors describe the mechanism.

The 2 asteroids involved

The following table gives you orbital and physical data relevant to these two bodies:

2008 EV5 2000 DP107 α
Semimajor axis 0.958 AU 1.365 AU
Eccentricity 0.083 0.377
Inclination 7.437° 8.672°
Orbital period 343 d 583 d
Spin period 3.725 h 2.775 h
Diameter 450 m 950 m

And you can see the shape model of 2008 EV5 on this video, from James Richardson:

They both are small bodies, which orbit in the vicinity of the Earth, and they spin fast. You cannot see that 2000 DP 107 α has a small companion, so this is the largest component (the primary) of a binary asteroid. Their proximity to the Earth made possible the acquisition of enough radar data to model their shapes. We know that they are top-shaped asteroid, i.e. they can be seen as two cones joined by their base, giving an equatorial ridge. Moreover, they both have an equatorial cavity, of diameters 160 and 400 m, and depths 20 and 60 meters, respectively. The authors estimate that given the numbers of potential projectiles in the NEO population, the odds are very small, i.e. one chance over 600, that these two craters are both consequences of impacts. Such an impact should have occurred during the last millions of years, otherwise the craters would have relaxed. This is why it must be the signature of another mechanism, here fission is proposed.

To have fission, you must spin fast enough, and this fast spin cannot be primordial, otherwise the asteroid would not have formed. So, something has accelerated the spin. This something is YORP, for Yarkovsky-O’Keefe-Radzievskii-Paddack.

Yarkovsky and YORP

When you are close enough to the Sun, the side facing the Sun warms, and then radiates in cooling. This is the Yarkovsky effect, which is a non-gravitational force, which affect the orbit of a small body. When you have an irregular shape, which is common among asteroids (you need to reach a critical size > 100 km to be pretty spherical), your response to the Sun light may be the one of a windmill to the wind. And your spin accelerates. This is the YORP effect.

These Yarkovsky and YORP effects have actually been measured in the NEO population.

Asteroid fission

When you spin fast enough, you just split. This is easy to figure out: the shape of a planetary body is a balance between its own gravity, its spin, and if applicable the tidal action of a large perturber. For our asteroids, we can neglect this last effect. So, we have a balance between the own gravity, which tends to preserve the asteroid, and the centrifugal force, which tends to destroy it. When you accelerate the rotation, you endanger the body. But it actually does not explode, since once some material is ejected, enough angular momentum is lost, and the two newly created bodies may survive. This process of fission is assumed to be the main cause of the formation of binaries in the NEO population.
2000 DP107 α belongs to a binary, while 2008 EV5 does not. But that does not mean that it did not experience fission, since the ejecta may not have aggregated, or the formed binary may not have survived as a binary.

Now, let us see how this process created an equatorial cavity.

Ejecting a protrusion

The author imagined that there was initially a mass filling the cavity. This mass would have had the same density as the remaining body, and they considered its size to be a free parameter. They assumed the smallest possible mass to exactly fill the cavity, the other options creating protrusion. As a consequence, the radius of the asteroid would have been larger at that very place, while it is smaller now. And this is where it is getting very interesting.

In accelerating the rotation of the asteroid, you move the surface limit, which would correspond to the balance between gravitation and spin. More exactly, you diminish its radius, until it reaches the surface of the asteroid… the first contact being at the protrusion. The balance being different whether you are inside or outside the asteroid, this limit surface would go deeper at the location of the protrusion, permitting the ejection of the mass which lies outside, and thus creating an equatorial cavity. Easy, isn’t it?

But this raises another question: this would mean that the cohesion at the equatorial plane is not very strong, and weaker than expected for an asteroid. How to solve this paradox? Thanks to kinetic sieving!

The kinetic sieving

The authors simulated a phenomenon that is known by geologist as reverse grading. In granular avalanches, the separation of particles occurs according to size, involving that the largest particles are expelled where the spin is faster, i.e. at the equator, which would result in a lowest tensile strength, which would itself facilitate the ejection of the mass, and create an equatorial cavity. This phenomenon has been simulated, but not observed yet. So, this is a prediction which should be tested by future space missions.

By the way, the size of the companion of 2000 DP107 α is consistent with a protruder of height 60m.

Summary

  1. Initial state: a Near-Earth Object, with irregular shape. Probably spins fast enough to be top-shaped, i.e. having an equatorial ridge,
  2. YORP accelerates the rotation, favoring the accumulation of large particles at the equator, while tropics are more sandy,
  3. A mass is ejected at the equator, leaving a cavity,
  4. You get a binary, which may survive or not.

More will be known in the next future, thanks to the space mission Osiris-REx, which will visit the asteroid (101955) Bennu in 2018 and return samples to the Earth in 2023. Does it have sandy tropics?

The Near-Earth Asteroid Bennu. © NASA.
The Near-Earth Asteroid Bennu. © NASA.

The study and the authors

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

The dynamics of the Quasi-Satellites

Hi there! After reading this post, you will know all you need to know on the dynamics of quasi-satellites. This is the opportunity to present you On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited, by Alexandre Pousse, Philippe Robutel and Alain Vienne. This study has recently been published in Celestial Mechanics and Dynamical Astronomy.

The 1:1 mean-motion resonance at small eccentricity

(see also here)

Imagine a pretty simple case: the Sun, a planet with a keplerian motion around (remember: its orbit is a static ellipse), and a very small third body. So small that you can neglect its mass, i.e. it does not affect the motion of the Sun and the planet. You know that the planet has no orbital eccentricity, i.e. the static ellipse serving as an orbit is actually a circle, and that the third body (let us call it the particle) has none either. Moreover, we want the particle to orbit in the same plane than the planet, and to have the same revolution period around the Sun. These are many conditions.
Under these circumstances, mathematics (you can call that celestial mechanics) show us that, in the reference frame which is rotating with the planet, there are two stable equilibriums 60° ahead and astern the planet. These two points are called L4 and L5 respectively. But that does not mean that the particle is necessary there. It can have small oscillations, called librations around these points, the resulting orbits being called tadpole orbits. It is even possible to have orbits enshrouding L4 and L5, this results in large librations orbits, called horseshoe orbits.

All of these configurations are stable. But remember: the planet is much less massive than the Sun, the particle is massless, the orbits are planar and circular… Things become tougher when we relax one of these assumptions. And the authors assumed that the particle had a significant eccentricity.

At high eccentricities: Quasi-satellites

Usually, increasing the eccentricity destabilizes you. This is still true here, i.e. co-orbital orbits are less stable when eccentric. But increasing the eccentricity also affects the dynamical structure of your problem in such a way that other dynamical configurations may appear. And this is the case here: you have an equilibrium where your planet lies.

Ugh, what does that mean? If you are circular, then your particle is at the center of your planet… Nope, impossible. But wait a minute: if you oscillate around this position without being there… yes, that looks like a satellite of the planet. But a satellite is under the influence of the planet, not of the star… To be dominated by the star, you should be far enough from the planet.

I feel the picture is coming… yes, you have a particle on an eccentric orbit around the star, the planet being in the orbit. And from the star, this looks like a satellite. Funny, isn’t it? And such bodies exist in the Solar System.

Orbit of a quasi-satellite. It follows the planet, but orbits the star.
Orbit of a quasi-satellite. It follows the planet, but orbits the star.

Known quasi-satellites

Venus has one known quasi-satellite, 2002 VE68. This is a 0.4-km body, which has been discovered in 2002. Like Venus, it orbits the Sun in 225 days, but has an orbital eccentricity of 0.41, while the one of Venus is 0.007. It is thought to be a quasi-satellite of Venus since 7,000 years, and should leave this configuration in some 500 years.

The Earth currently has several known quasi-satellites, see the following table:

(277810) 2006 FV350.387.1°10,000 y2013 LX280.4550°40,000 y2014 OL3390.4610.2°1,000 y(469219) 2016 HO30.107.8°400 y

Known quasi-satellites of the Earth
Name Eccentricity Inclination Stability
(164207) 2004 GU9 0.14 13.6° 1,000 y

These bodies are all smaller than 500 meters. Because of their significant eccentricities, they might encounter a planet, which would then affect their orbits in such a way that the co-orbital resonance would be destabilized. However, significant inclinations limit the risk of encounters. Some bodies switch between quasi-satellite and horseshoe configurations.

Here are the known quasi-satellites of Jupiter:

Known quasi-satellites of Jupiter
Name Eccentricity Inclination Stability
2001 QQ199 0.43 42.5° > 12,000 y
2004 AE9 0.65 1.6° > 12,000 y
329P/LINEAR-Catalina 0.68 21.5° > 500 y
295P/LINEAR 0.61 21.1° > 2,000 y

329P/LINEAR-Catalina and 295P/LINEAR being comets.

Moreover, Saturn and Neptune both have a confirmed quasi-satellite. For Saturn, 2001 BL41 should leave this orbit in about 130 years. It has an eccentricity of 0.29 and an inclination of 12.5°. For Neptune, (309239) 2007 RW10 is in this state since about 12,500 years, and should stay in it for the same duration. It has an orbital eccentricity of 0.3, an inclination of 36°, and a diameter of 250 km.

Understanding the dynamics

Unveiling the dynamical/mathematical structure which makes the presence of quasi-satellites possible is the challenge accepted by the authors. And they succeeded. This is based on mathematical calculation, in which you write down the equations of the problem, you expand them to retain only what is relevant, in making sure that you do not skip something significant, and you manipulate what you have kept…

The averaging process

The first step is to write the Hamiltonian of the restricted planar 3-body problem, i.e. the total energy of a system constituted by the Sun, the planet, and the massless particle. The dynamics is described by so-called Hamiltonian variables, which allow interesting mathematical properties…
Then you expand and keep what you need. One of the pillars of this process is the averaging process. When things go easy, i.e. when your system is not chaotic, you can describe the dynamics of the system as a sum of sinusoidal contributions. This is straightforward to figure out if you remember that the motions of the planets are somehow periodic. Somehow means that these motions are not exactly sinusoidal, but close to it. So, you expand it in series, in which other sinusoids (harmonics) appear. And you are particularly interested in the one involving λ-λ’, i.e. the difference between the mean longitude of the planet and the particle. This makes sense since they are in the co-orbital configuration, that particular angle should librate with pretty small oscillations around a given value, which is 60° for tadpole orbits, 180° for horseshoes, and 0° for quasi-satellites. Beside this, you have many small oscillations, in which you are not interested. Usually you can drop them in truncating your series, but actually you just average them, since they average to 0. This is why you can drop them.
To expand in series, you should do it among a small parameter, which is usually the eccentricity. This means that your orbit looks pretty like a circle, and the other terms of the series represent the difference with the circle. But here there is a problem: to get quasi-satellite orbits, your eccentricity should be large enough, which makes the analytical calculation tougher. In particular, it is difficult to guarantee their convergence. The authors by-passed this problem in making numerical averaging, i.e. they computed numerically the integrals of the variables of the motion over an orbital period.

Once they have done this, they get a simplified system, based on one degree-of-freedom only. This is a pair of action-angle variables, which will characterize your quasi-satellite orbit. This study also requires to identify the equilibriums of the system, i.e. to identify the existing stable orbits.

Perspectives

So, this study is full of mathematical calculations, aiming at revisiting this problem. The authors mention as possible perspective the study of resonances between the planets, which disturb the system, and the proper frequency of the quasi-satellite orbit. This is the oscillating frequency of the angle characterizing the orbit, and if it is equal to a frequency already present in the system, it could have an even more interesting dynamics, e.g. transit between different states (quasi-satellite / horsehoe,…).

To know more…

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Our water comes from far away

Hi there! Can you imagine that our water does not originally come from the Earth, but from the outer Solar System? The study I present you today explains us how it came to us. This is Origin of water in the inner Solar System: Planetesimals scattered inward during Jupiter and Saturn’s rapid gas accretion by Sean Raymond and Andre Izidoro, which has recently been published in Icarus.

From the planetary nebula to the Solar System

There are several competing scenarios, which describe a possible path followed by the Solar System from its early state to its current one. But all agree that there was originally a protoplanetary disk, orbiting our Sun. It was constituted of small particles and gas. Some of the small particles accreted to form the giant planets, first as a massive core, then in accreting some gas around. The proto-Jupiter cleared a ring-shaped gap around its orbit in the disk, Saturn formed as well, the planets migrated, in interacting with the gas. How fast did they migrate? Inward? Outward? Both? Scenarios diverge. Anyway, the gas was eventually ejected, and the protoplanetary disk was essentially cleared, except when it is not. There remains the telluric planets, the giant planets, and the asteroids, many of them constituting the Main Belt, which lies between the orbits of Mars and Jupiter.
If you want to elaborate a fully consistent scenario of formation / evolution of the Solar System, you should match the observations as much as possible. This means matching the orbits of the existing objects, but not only. If you can match their chemistry as well, that is better.

No water below this line!

The origin of water is a mystery. You know that we have water on Earth. It seems that this water comes from the so-called C-type asteroids. These are carbonaceous asteroids, which contain a significant proportion of water, usually between 5 and 20%. This is somehow the same water as on Earth. In particular, it is consistent with the ratios D/H and 15N/14N present in our water. D is the deuterium, it is an isotope of hydrogen (H), while 15N and 14N are two isotopes of nitrogen (N).

These asteroids are mostly present close to the outer boundary of the Main Belt, i.e. around 3.5 AU. An important parameter of a planetary system is the snow line: below a given radius, the water cannot condensate into ice. That makes sense: the central star (in our case, the Sun) is pretty hot (usually more than pretty, actually…), and ice cannot survive in a hot environment. So, you have to take some distance. And the snow line of the Solar System is currently lose to 3.5 AU, where we can find these C-type asteroids. Very well, there is no problem…

But there is one: the location of the snow line changes during the formation of the Solar System, since it depends on the dynamical structure of the disk, i.e. eccentricity of the particles constituting it, turbulence in the gas, etc. in addition to the evolution of the central star, of course. To be honest with you, I have gone through some literature and I cannot tell you where the snow line was at a given date, it seems to me that this is still an open question. But the authors of this study, who are world experts of the question, say that the snow line was further than that when these C-types asteroids formed. I trust them.

And this raises an issue: the C-types asteroids, composed of at least 5% of water, have formed further than they are. This study explains us how they migrated inward, from their original location to their present one.

Planet encounter and gas drag populate the Asteroid Belt

The authors ran intensive numerical simulations, in which the asteroids are massless particles, but with a given radius. This seems weird, but this just means that the authors neglected the gravitational action of the asteroids on the giant planets. The reason why they gave them a size in that it influences the way the gas drag (remember: the early Solar System was full of gas) affects their orbits. This size actually proved to be a key parameter. So, these asteroids were affected by the gas and the giant planets, but in the state they were at that time, i.e. initially Jupiter and Saturn were just slowly accreting cores, and when these cores of solid material reached a critical size, then they were coated by a pretty rapid (over a few hundreds of kyr) accretion of gas. The authors considered only Jupiter in their first simulations, then Jupiter and Saturn, and finally the four giant planets. Their different parameters were:

  • the size of the asteroids (planetesimals),
  • the accretion velocity of the gas around Jupiter and Saturn,
  • the evolution scenario of the early Solar System. In particular, the way the giant planets migrated.

Simulating the formation of the planet actually affects the orbital evolution of the planetesimals, since the mass of the planets is increasing. The more massive the planet, the most deviated the asteroid.

And the authors succeed in putting C-type asteroids with this mechanism: when a planetesimal encounters a proto-planet (usually the proto-Jupiter), its eccentricity reaches high numbers, which threatens its orbital stability around the Sun. But the gas drag damps this eccentricity. So, these two effects compete, and when ideally balanced this results in asteroids in the Main-Belt, on low eccentric orbits. And the authors show that this works best for mid-sized asteroids, i.e. of the order of a few hundreds of km. Below, Jupiter ejects them very fast. Beyond, the gas drag is not efficient enough to damp the eccentricity. And this is consistent with the current observations, i.e. there is only one C-type asteroid larger than 1,000 km, this is the well-known Ceres.

However, the scenarios of evolution of the Solar System do not significantly affect this mechanism. So, it does not tell us how the giant planets migrated.

Once the water ice has reached the main asteroid belt, other mechanism (meteorites) carry it to the Earth, where it can survive thanks to our atmosphere.

Making the exoplanets habitable

This study proposes a mechanism of water delivery, which could be adapted to any planetary system. In particular, it tells us a way to make exoplanetary planets habitable. Probably more to come in the future.

To know more…

  • The study, presented by the first author (Sean N. Raymond) on his own blog,
  • The website of Sean N. Raymond,
  • The IAU page of Andre Izidoro.
  • And I would like to mention Pixabay, which provides free images, in particular the one of Cape Canaveral you see today. Is this shuttle going to fetch some water somewhere?

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

An asteroid pair

Hi there! Today I present you the study of an asteroid pair. Not a binary, a pair. A binary asteroid is a couple of asteroids which are gravitationally bound, while in pair, the asteroids are just neighbors, they do not live together… but have. The study is entitled Detailed analysis of the asteroid pair (6070) Rheinland and (54287) 2001 NQ8, by Vokrouhlický et al., and it has recently been published in The Astronomical Journal.

Asteroid pairs

I have presented asteroid families in a previous post. These are groups of asteroids which present common dynamical and physical properties. They can be in particular identified from the clustering of their proper elements, i.e. you express their orbital elements (semimajor axis, eccentricity, inclination, pericentre, …), you treat them properly so as to get rid off the gravitational disturbance of the planets, and you see that some of these bodies tend to group. This suggests that they constitute a collisional family, i.e. they were a unique body in the past, which has been destroyed by collisions.
An asteroid pair is something slightly different, since these are two bodies which present dynamical similarities in their osculating elements, i.e. before denoising them from the gravitational attraction of the planets. Of course, they would present similarities in their proper elements as well, but the fact that similarities can be detected in the osculating elements means that they are even closer than a family, i.e. the separation occurred later. Families younger than 1 Myr (1 million of years) are considered to be very young; the pair I present you today is much younger than that. How much? You have to read me before.
A pair suggests that only two bodies are involved. This suggests a non-collisional origin, more particularly an asteroid fission.

Asteroid fission

Imagine an asteroid with a very fast rotation. A rotation so fast that it would split the asteroid. We would then have two components, which would be gravitationally bound, and evolving… Depending on the energy involved, it could remain a stable binary asteroid, a secondary fission might occur, the two or three components may migrate away from each other… and in that case we would pair asteroid with very close elements of their heliocentric orbits.
It is thought that the YORP (Yarkovsky – O’Keefe – Radzievskii – Paddack) could trigger this rotational fission. This is a thermic effect which alter the rotation, and in some cases, in particular when the satellite has an irregular shape, it could accelerate it. Until fission.
Thermic effects are particularly efficient when the Sun is close, which means that NEA (Near Earth Asteroids) are more likely to be destroyed by this process than Main Belt asteroids. Here, we deal with Main Belt asteroids.

The pair 6070-54827 (Rheinland – 2001 NQ8)

The following table present properties of Rheinland and 2001 NQ8. The orbital elements are at Epoch 2458000.5, i.e. September 4th 2017. They come from the JPL Small-Body Database Browser.

(6070) Rheinland (54827) 2001 NQ8
Semimajor axis (AU) 2.3874015732216 2.387149297807496
Eccentricity 0.2114524962733347 0.211262507795103
Inclination 3.129675305535938° 3.128927421642917°
Node 83.94746016534368° 83.97704257098502°
Pericentre 292.7043398319871° 292.4915004062336°
Orbital period 1347.369277588708 d (3.69 y) 1347.155719572348 d (3.69 y)
Magnitude 13.8 15.5
Discovery 1991 2001

Beside their magnitudes, i.e. Rheinland is much brighter than 2001 NQ8, this is why it was discovered 10 years earlier, we can see that all the slow orbital elements (i.e. all of them, except the longitude) are very close, which strongly suggests they shared the same orbit. Not only their orbits have the same shape, but they also have the same orientation.

Shapes and rotations from lightcurves

A useful tool for determining the rotation and shape of an asteroid is the lightcurve. The object reflects the incident Solar light, and the way it reflects it will tell us something on its location, its shape, and its orientation. You can imagine that the surfaces of these bodies are not exclusively composed of smooth terrain, and irregularities (impact basins, mountains,…) will result in a different Solar flux, which also depends on the phase, i.e. the angle between the normale of the surface and the asteroid – Sun direction… i.e. depends whether you see the Sun at the zenith or close to the horizon. This is why recording the light from the asteroid at different dates tell us something. You can see below an example of lightcurve for 2001 NQ8.

Example of lightcurve for 2001 NQ8, observed by Vokrouhlický et al.

Recording such a lightcurve is not an easy task, since the photometric measurements should be denoised, otherwise you cannot compare them and interpret the lightcurve. You have to compensate for the variations of the luminosity of the sky during the observation (how far is the Moon?), of the thickness of the atmosphere (are we close to the horizon?), of the heterogeneity of the CCD sensors (you can compensate that in measuring the response of a uniform surface). And the weather should be good enough.

Once you have done that, you get a lightcurve alike the one above. We can see 3 maxima and 2 minima. Then the whole set of lightcurves is put into a computational machinery which will give you the parameters that best match the observations, i.e. periods of rotation, orientation of the spin pole at a given date, and shape… or at least a diameter. In this study, the authors already had the informations for Rheinland but confirmed them with new observations, and produced the diameter and rotation parameters for 2001 NQ8. And here are the results:

Spin pole(124°,-87°)(72°,-49°) or (242°,-46°)

(6070) Rheinland (54827) 2001 NQ8
Diameter (km) 4.4 ± 0.6 2.2 ± 0.3
Spin period (h) 4.2737137 ± 0.0000005 5.877186 ± 0.000002

We can see rapid rotation periods, as it is often the case for asteroids. The locations of the poles mean that their rotations
are retrograde, with respect to their orbital motions. Moreover, two solutions best match the pole of 2001 NQ8.

Dating the fission

The other aspect of this study is a numerical simulation of the orbital motion of these two objects, backward in time, to date their separation. Actually, the authors considered 5,000 clones of each of the two objects, to make their results statistically relevant.
They not only considered the gravitational interactions with other objects of the Solar System, but also the Yarkovsky effect, i.e. a thermal pull due to the Sun, which depends on the reflectivity of the asteroids, and favors their separation. For that, they propose new equations implementing this effect. They also simulated the variations of the spin pole orientation, since it affects the thermal acceleration.

And here is the result: the fission probably occurred 16,340 ± 40 years ago.

Perspectives

Why doing that? Because what we see is the outcome of an asteroid fission, which occurred recently. The authors honestly admit that this result could be refined in the future, depending on

  • Possible future measurements of the Yarkovsky acceleration of one or two of these bodies,
  • The consideration of the mutual interactions between Rheinland and 2001 NQ8,
  • Refinements of the presented measurements,
  • Discovery of a third member?

To date the fission, they dated a close approach between these two bodies. They also investigated the possibility that that
close approach, some 16,000 years from now, could have not been the right one, and that the fission could have been much older. For that, they ran long-term simulations, which suggest that older close approaches should have been less close: if the pair were older, Yarkovsky would have separated it more.

To know more

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