Tag Archives: Yarkovsky

Thermal effects affect the rotation of asteroids

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.

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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Indirect measurement of an asteroid’s pole

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.

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)),


  • 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.