Category Archives: Asteroids: Near-Earth Objects

Asteroids: Near-Earth Objects

Thermal effects affect the rotation of asteroids

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Hi there! Today we discuss the rotation of asteroids. You know, these small bodies are funny. When you are a big body, you are just attracted by your siblings. The Sun, the planets, etc. But when you are a small body, your life may be much more chaotic! Such small bodies not only experience the influence of gravitational perturbations, but also of thermal effects, especially when they are close enough to the Sun (Near-Earth Objects). Not only you have radiation pressure of the Sun, due to the electromagnetic field, but also a torque due to the difference of temperature between different areas of the surface of the small body.
Investigating such effects is particularly tough, since it depends on the shape of the asteroid, which could be anything. Shape, surface rugosity, thermal inertia… and the rotation state as well. When you face the Sun, you heat, but with a delay… and meanwhile, you do not face the Sun anymore… you see the nightmare for planetary scientists? Well, actually, you can say that it is not a nightmare, but something fascinating instead. You bypass such difficulties by making simplified models, and if you have the opportunity to compare with real data, i.e. observations, then you have a chance to validate your theory.
Today I present Systematic structure and sinks in the YORP effect, by Oleksiy Golubov and Daniel J. Scheeres. This study, published in The Astronomical Journal, tells us that sometimes the thermal effects may stabilize the rotational state of the asteroids.

Outline

Yarkovsky and YORP
YORP cycles
Normal and tangential YORP
New equilibriums in the rotational state
Testing the prediction
The study and its authors

Yarkovsky and YORP

As I said, the most important of the thermal effects, which are experienced by small asteroids (up to some 50 km), is the Yarkovsky effect. The area which faces the Sun heats, and then reemits photons while cooling. The reemission of these photons pushes the asteroids in a direction, which depends on the rotation of the body. As a consequence, this makes the prograde asteroids (rotation in the same direction as the orbit) spiral outward, while the retrograde ones spiral inward. The consequence on the orbits is a secular drift of the semimajor axis, which has been measured in some cases.
The first measurement dates back to 2003. The small asteroid (530 m) 6489 Golevka drifted by 15 km since 1991, with respect to the orbital predictions, which considered only the gravitational perturbations of the surrounding objects.
This effect had been predicted around 1900 by the Polish civil engineer Ivan Osipovich Yarkovsky.

And now: YORP. YORP stands for Yarkovsky-O’Keefe-Radzievskii-Paddack, i.e. 4 scientists. This is the thermal effect on the rotation. Most of the asteroids have irregular shapes, i.e. they do not look like ellipsoids, but rather like… anything else. Which means that the reemission of photons would not average to 0 over a rotational (or spin) period. As a consequence, if the asteroid is like a windmill, then its rotation will accelerate. Rotational data on Near-Earth Asteroids smaller than 50 km show an excess of fast rotators, with respect to larger bodies. And theoretical studies have shown that YORP could ultimately destroy an asteroid, in making it spin so fast that it would become unstable. The outcome would then be a binary object.

This is anyway a very-long-term effect.

YORP cycles

In fact, when the rotational energy is not high enough to provoke the disruption of the asteroid, the theory of YORP predicts that the rotational states experience cycles, over several hundreds of thousands years. During these cycles, the asteroid switches from a tumbling state, i.e. rotation around 3 axes to the rotation around one single axis, and then goes back to the tumbling states. These are the YORP cycles, which are not really observed given their long duration. But the authors of this study tell us that these cycles may be disrupted.

Normal and tangential YORP

The authors recall us that the YORP effect, which generates these cycles, is in fact the normal YORP. There is a tangential YORP as well. This tangential YORP (TYORP) is due to heat transfer effects on the surface, which results in asymmetric light emission. This yields an additional force, which alters the rotation.

New equilibriums in the rotational state

And the consequence is this: when you add the TYORP in simulating the rotational dynamics of your asteroid, you get equilibriums, i.e. rotational state, which would remain constant with respect to the time. In other words, under some circumstances, the rotational state leaves the YORP cycles, to remain locked in a given state. These states would have a principal rotation axis, which would be either parallel to the orbit, or orthogonal. In this last case, the rotation could either be prograde or retrograde.

Testing the prediction

This study suggests that the authors have predicted a rotation state. It would be good to be able to test this prediction, i.e. observe this rotation state among the asteroids.
The study does not mention any observable evidence of this theory. As the authors honestly say, this is only a first taste of the complicated theory of the YORP effect. Additional features should be considered, and the mechanism of trapping into these equilibriums is not investigated… or not yet.

Anyway, this is an original study, a new step to the full understanding of the YORP effect.

The study and its authors

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Asteroids: Near-Earth Objects

The Earth will encounter Apophis

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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.

Outline

The asteroid (99942) Apophis
Potentially Hazardous Asteroids
A close encounter changes the dynamics
The rotation is critical
A numerical study
Different obliquity, same spin rate
The study and its authors

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.

Asteroids: Near-Earth Objects

Rough terrains spin up asteroids

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Hi there! If you follow me, you have already heard of the Yarkovsky effect, or even of the YORP, which are non-gravitational forces affecting the dynamics of Near-Earth Asteroids. Today I tell you about the TYORP, i.e. the Tangential YORP. This is the opportunity for me to present you Analytic model for Tangential YORP, by Oleksiy Golubov. This study has recently been published in The Astronomical Journal. The author meets the challenge to derive an analytical formula for the thermal pressure acting on the irregular regolith of an asteroid. Doing it requires to master the physics and make some sound approximations, following him tells us many things on the Tangential YORP.

Outline

From Yarkovsky to TYORP
Modeling the physics
A perturbative treatment
Validation
Perspectives
The study and its author

From Yarkovsky to TYORP

When we address the dynamics of Near-Earth Asteroids, we must consider the proximity of the Sun. This proximity involves thermal effects, which significantly affect the dynamics of such small bodies. In other words, the dynamics is not ruled by the gravitation only. The main effect is the Yarkovsky effects, and its derivatives.

Yarkovsky

The Sun heats the surface of the asteroid which faces it. When this surface element does not face the Sun anymore, because of the rotation of the asteroid, it cools, and radiates some energy. This effect translates into a secular drift in the orbit, which is known as the Yarkovsky effect. This Yarkovsky effect has been directly measured for some asteroids, in comparing the simulated orbit from a purely gravitational simulation, with the astrometric observations of the objects. Moreover, long-term studies have shown that the Yarkovsky effect explains the spreading of some dynamical families, i.e. asteroids originating from a single progenitor. In that sense, observing their current locations proves the reality of the Yarkovsky effect.
When the asteroid has an irregular shape, which is common, the thermal effect affects the rotation as well.

YORP

Cooling a surface element which has been previously heated by the Sun involves a loss of energy, which depends on the surface itself. This loss of energy affects the rotational dynamics, which is also affected by the heating of some surface. But for an irregular shaped body, the loss and gain of energy does not exactly balance, and the result is an asteroid which spins up, like a windmill. In some cases, it can even fission the body (see here). This effect is called YORP, for Yarkovsky-O’Keefe–Radzievskii–Paddack.

This is a large-scale effect, in the sense that it depends on the shape of the asteroid as a whole. Actually, the surface of an asteroid is regolith, it can have boulders… i.e. high-frequency irregularities, which thus will be heated differently, and contribute to YORP… This contribution is known as Tangential YORP, or TYORP.

Modeling the physics

When you heat a boulder from the Sun, you create an inhomogeneous elevation of temperature, which can be modeled numerically, with finite elements. For an analytical treatment, you cannot be that accurate. This drove the author to split the boulder into two sides, the eastern and the western sides, both being assumed to have an homogeneous temperature. Hence, two temperatures for the boulder. Then the author wrote down a heat conduction equation, which says that the total heat energy increase in a given volume is equal to the sum of the heat conduction into this volume, the direct solar heat absorbed by its open surface, and the negative heat emitted by the open surface (which radiates).

These numbers depend on

  • the heat capacity of the asteroid,
  • its density,
  • its heat conductivity,
  • its albedo, i.e. its capacity to reflect the incident Solar light,
  • its emissivity, which characterizes the radiated energy,
  • the incident Solar light,
  • the time.

The time is critical since a surface will heat as long it is exposed to the Sun. In the calculations, it involves the spin frequency. After manipulation of these equations, the author obtains an analytical formula for the TYORP pressure, which depends on these parameters.

A perturbative treatment

In the process of solving the equations, the author wrote the eastern and western temperatures as sums of periodic sinusoidal solutions. The basic assumption, which seems to make sense, is that these two quantities are periodic, the period being the rotation period, P, of the asteroid. This implicitly assumes that the asteroid rotates around only one axis, which is a reasonable assumption for a general treatment of the problem.
As a result, the author expects these two temperatures to be the sum of sines and cosines of periods P/n, P being an integer. For n=1, you have a variation of period P, i.e. a diurnal variation. For n = 2, you have a semi-diurnal one, etc.

The perturbative treatment of the problem consists in improving the solution in iterating it, first in expressing only one term, i.e. the diurnal one, then in using the result to derive the second term, etc. This assumes that these different terms have amplitudes, which efficiently converge to 0, i.e. the semi-diurnal effect is supposed to be negligible with respect to the diurnal one, but very large with respect to the third-diurnal, etc. Writing down the solution under such a form is called Fourier decomposition.

The author says honestly that he did not check this convergence while solving the equation. However, he successfully tested the validity of his obtained solution, which means that the resolution method is appropriate.

Validation

The author is active since many years on the (T)YORP issue, and has modeled it numerically in a recent past. So, validating his analytical formula consisted in confronting it with his numerical results.

He particularly confronted the two results in the cases of a wall, a half buried spherical boulder, and a wave in the regolith, with respect to physical characteristics of the material, i.e. dimension and thermic properties. Even though visible differences, the approximation is pretty good, validating the methodology.

This allowed then the author to derive an analytical formula of the TYORP pressure on a while regolith, which is composed of boulders, which sizes are distributed following a power law.

Perspectives

This is the first analytical formula for the TYORP, and I am impressed by the author’s achievement. We can expect in the future that this law (should we call it the Golubov law?) would be a reference to characterize the thermic properties of an asteroid. In other words, future measurements of the TYORP effect could give the thermic properties, thanks to this law. This is just a possibility, which depends on the reception of this study by the scientific community, and on future studies as well.

The study and its author

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

Asteroids: Near-Earth Objects

Indirect measurement of an asteroid’s pole

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Hi there! Today, another paper on the Yarkovsky effect. You know, this non-gravitational force which acts on the asteroid, especially if it is close enough to the Sun. After reading this post, you will know how it can reveal us the obliquity of an asteroid. I present you Constraints on the near-Earth asteroid obliquity distribution from the Yarkovsky effect, by C. Tardioli, D. Farnocchia, B. Rozitis, D. Cotto-Figueiroa, S.R. Chesley, T.S. Statler & M. Vasile. This paper has recently been accepted for publication in Astronomy and Astronomy.

Outline

The way it works
The rotation of an asteroid
Yarkovsky: A thermal effect
Measuring Yarkovsky
So many retrograde asteroids
The study and the authors

The way it works

Imagine you want to know the rotation of an asteroid… but you cannot measure it directly. However, you can measure the orbital motion of the asteroid, with enough accuracy to detect an effect (here Yarkovsky), which itself depends on the rotation… measuring Yarkovsky is measuring the rotation! Easy, isn’t it?

The rotation of an asteroid

As any planetary body, an asteroid has a rotational motion, which consists in spinning around one axis (actually 3, but you can safely neglect this fact), at a given rate. We can consider that we know its rotation when

  1. We know its spin rate, or its rotational period (let us assume it is constant),
  2. We know the orientation of its spin pole. We will call it the obliquity.

Usually the asteroids spin in a few hours, which is very fast since they need at least several months to complete one revolution around the Sun. The obliquity is between 0° and 180°. 0° means that the spin axis is orthogonal to the orbital plane, and that the rotation is prograde. However, 180° is the other extreme case, the spin axis is orthogonal, but with a retrograde rotation.

A direct measurement of these two quantities would consist in following the surface of the asteroid, to observe the rotation. Usually we cannot observe the surface, but sometimes we can measure the variations of the magnitude of the asteroid over time. This is directly due to the Solar light flux, which is reflected by the surface of the asteroid. Because the topography is irregular, the rotation of the asteroid induces variations of this reflection, and by analyzing the resulting lightcurve we can retrieve the rotational quantities.

Very well, but sometimes the photometric observations are not accurate enough to get these quantities. And other times, the measured rotational quantities present an ambiguity, i.e. 2 solutions, which would need an independent measurement to discriminate them, i.e. determine which of the two possible results is the right one.

It appears that the Yarkovsky effect, which is an alteration of the orbital motion of the body due to the inhomogeneity of its temperature, itself due to the Solar incident flux and the orientation of the body, i.e. its rotation, can sometimes be measured. When you know Yarkovsky, you know the obliquity. Well, it is a little more complicated than that.

Yarkovsky: A thermal effect

Since I have already presented you Yarkovsky with words, I give you now a formula.

The Yarkovsky effect, i.e. the thermal heating of the asteroid, induced a non-gravitational acceleration of its orbital motion. This acceleration reads A2/r2, where r is the distance to the Sun (remember that the asteroid orbits the Sun), and

A2 = 4/9(1-A)Φ(αf(θs)cos(ε)-f(θo)sin2(ε)),

where

  • A: albedo of the asteroid, i.e. quantity of the reflected light wrt the incident one,
  • Φ: Solar radiation,
  • α: an enhancement factor. This is a parameter…
  • ε: the obliquity (which the authors determined),
  • θs / θo: thermal parameters which depend on the spin period (s), and the orbital one (o), respectively.

If you know Yarkovsky, you know A2, since you know the distance r (you actually know where the asteroid is). If you know all the parameters except ε, then A2 gives you ε. In fact, some of the other parameters need to be estimated.

Measuring Yarkovsky

As you can see, this study is possible only for asteroids, for which you can know the Yarkovsky acceleration. Since it is a thermal effect, you can do it only for Near-Earth Asteroids, which are closer to the Sun than the Main Belt. And to measure Yarkovsky, you must simulate the orbital motion of the asteroid, which is perturbed by the main planets and Yarkovsky, with the Yarkovsky acceleration as a free parameter. A fit of the simulations to the actual astrometric observations of the asteroid gives you a number for the Yarkovsky acceleration, with a numerical uncertainty. If your number is larger than the uncertainty, then you have detected Yarkovsky. And this uncertainty mainly depends on the accuracy of your astrometric observations. It could also depend on the validity of the dynamical model, i.e. on the consideration of the forces perturbing the orbital motion, but usually the dynamical model is very accurate, since the masses and motions of the disturbing planets are very well known.
The first detection of the Yarkovsky acceleration was in 2003, when a drift of 15 km over 12 years was announced for the asteroid 6489 Golevka.

So, you have now a list of asteroids, with their Yarkovsky accelerations. The authors worked with a final dataset of 125 asteroids.

So many retrograde asteroids

The authors tried to fit a distribution of the obliquities of these asteroids. The best fit, i.e. which reduces the distance between the resulting obliquities and the Yarkovsky acceleration that they would have produced, is obtained from a quadratic model, i.e. 1.12 cos2(ε)-0.32 cos(ε)+0.13, which is represented below.

Distribution of the asteroids with respect to their obliquity.
Distribution of the asteroids with respect to their obliquity.

What you see is the number of asteroids with respect to their obliquity. The 2 maxima at 0° and 180° mean that most of the asteroids spin about an axis, which is almost orthogonal to their orbital plane. From their relative heights, it appears that there about twice more retrograde asteroids than prograde ones. This is consistent with previous studies, these obliquities actually being a consequence of the YORP effect, which is the influence of Yarkovsky on the rotation.

The study 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.

Asteroids: Near-Earth Objects

Equatorial cavities due to fissions

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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.

Outline

The 2 asteroids involved
Yarkovsky and YORP
Asteroid fission
Ejecting a protrusion
The kinetic sieving
Summary
The study and the authors

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.