The Yarkovsky Effect
Published on Oct 30, 2006 at 4:36 pm.
6 Comments.
Filed under asteroids, physics.
In my second semester physics classes, we discuss how light sometimes acts like particles. Light ”particles” are called photons.  A photon of light can carry momentum like any particle. Thus, when an object it emits light, it must have some sort of “recoil”. Likewise, when photons strike something, they impart momentum to it just as if they were tiny little bits of matter striking the object. This is the basis of solar sails, a method of propulsion using just the light from the Sun to move a spacecraft around.
The idea that light can exert a force on anything seems strange to most people. But, it really does happen! In fact, the largest and brightest stars are in part limited in terms of how big they can be before they tear themselves apart from their own light emissions! Likewise, black holes can only eat so much stuff at once, because an accretion disk that has too much stuff in it becomes so hot and bright that it blows itself away.
Obviously though, the force of light is normally pretty small. the cases that I listed in the previous paragraph are extreme cases. You don’t turn on a flashlight and feel your hand jerk backward from the recoil. Likewise, you don’t get bowled over by the sunlight hitting you as you step outdoors on a bright sunny summer day. But, small forces can add up over time.
Ion propulsion, which has been used for NASA’s Deep Space 1 craft and ESA’s Smart 1, is a case of a small force adding up to something big after a while. Ion propulsion uses very high speed particles shooting out from a spacecraft’s engine. There is very little thrust, but over time it adds up, and if you don’t mind waiting a long time to get going, you can wind up going pretty fast with relatively little propellant. Ion propulsion is not light pressure, but there has been talk about using high power lasers as engines for long range spacecraft. Again, there is very little thrust, as neither ions nor light can push very hard at the intensities that we can achieve with our present technology, but the thrust can be sustained for a very long time, and over time it adds up.
This is at the heart of something that we call the Yarkovsky effect (named for Ivan Yarkovsky, who described the phenominon a little over a century ago). He noted that asteroids could experience a tiny push that, while not amounting to much over the short term, could lead to long term dramatic changes in the asteroids’ orbits.
Yarkovsky noted that rotating asteroids would have have one side warmer than the other. The warmer a body, the more electromagnetic radiation that it emits.  The temperatures of asteroids are such that this radiation is primarily infrared radiation. As asteroids rotate, the side towards the Sun gets warmer, and the side away from the Sun cools off.  So, as the asteroid orbits the Sun, the side that has just turned away from the Sun is warmer than the side that is just turning towards the Sun. As long as the rotational axis of the asteroid is not inclined nearly perpendicular to the axis of its orbit, then this means that either the leading side or trailing side of the asteroid in its orbit will be warmer than the other side (whether it is leading or trailing depends upon whether the asteroid rotates prograde, as in my diagram, or retrograde, meaning that it rotates in the opposite angular sense from that of its orbit).  Now, the warmer that an object is, the more thermal radiation that it emits. So, the warmer side will be emitting slightly more infrared light than the cooler side.  This means that there will be a tiny bit more force pushing on the warm side than on the cool side. To even further add to the effect, the frequency of light emitted is also slightly higher on the warm side than on the cool side. Higher frequency light has a bigger momentum than lower frequency light.Â
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In my drawing here, the asteroid will experience a slightly greater force pushing on the trailing side than on the leading side. The anisotropy will be tiny — hardly measurable at all. But, over time, it will gradually push the asteroid into an orbit that gradually gets farther from the Sun. If the asteroid were to rotate in the other direction, then the anisotropy will be reversed, and the asteroid will experience a greater force on the leading side than the trailing side, gradually pushing the asteroid towards the Sun. Actually computing this effect can be exceedingly difficult. It depends upon the nature of the surface of the asteroid and the emissivity of that surface (a measure of how efficient of a thermal radiator the surface is). It also depends upon the degree of solar heating, and that depends upon the albedo of the surface (how reflective it is). The solar heating also can vary with distance from the Sun, so the Yarkovsky effect would also depend on the asteroid’s orbital eccentricity (how elliptical the orbit is). The magnitude of the effect would even be changed by the seasonal orientation of the asteroid’s rotational axis.  There are several other factors, as well, that would make the effect larger or smaller over time. So, really computing the effect is tough.
When Yarkovsky set forth his ideas, he wasn’t really taken very seriously at first. A decade later, though, some astronomers began to suggest that this effect might actually make a difference over the long term. The effect is tiny, for sure. It amounts to such a tiny effect that it would be no more than a few hundredths of a pound of force on an average asteroid. For a body the size of an asteroid, that is next to nothing. But next to nothing is not the same thing as nothing.
A force that tiny would have an imperceptible effect on the asteroid over a short time. But, remember that asteroids are orbiting the Sun for a long time. Over millions or billions of years, such effects can add up to major shifts in an asteroid’s orbit. It can cause asteroids that are safely in the asteroid belt to drift inward to where they cross the orbits of the inner planets (including Earth). Or, this tiny push over time can push an asteroid into a region where Jupiter’s gravity tends to toss them into chaotic orbits (the asteroid belt’s Kirkwood gaps), which can also intersect Earth’s orbit.
But, you might say that this is all theory. Is there any proof that the Yarkovsky effect does, in fact, exist? Yes, there is. In a paper published in the journal Science in 2003, Clesley, Ostro, et al. report their measurements of the Yarkovsky effect on the asteroid 6489 Golevka. Careful radar ranging measurements of Golevka in 1991, 1995, 1999, and 2003 showed that the asteroid’s orbit has been shifted by about 9.4 miles. That isn’t much in the scheme of things for the Solar System, but remember that that was only over 12 years. Over millions of years, then the orbital shift can be quite extreme. So, the Yarkovsky effect is real. And this makes computing the future positions of asteroids an even more losing proposition than it already is. They simply move around too much. And comets are even worse, since they have jets of material shooting out of them that further alter their orbits.Â
-Astroprof
(Asteroid image credit:Â NASA)
Zavatar on October 30, 2006 at 6:10 pm: 1
Once again a great post. I had read about the Yarkovsky effect before, but I think this is the first time I’ve actually understood it. One question, though: can this affect planets? They are much bigger than an asteroid, yes, but that also means they have a larger area that can emit radiation…right?
Astroprof on October 30, 2006 at 9:34 pm: 2
Thanks, Zavatar.
In principle, planets would experience the same thing, but the larger the body, the smaller the effect. If you double the radius, you get four times the area, but eight times the amount of stuff to move around. That would mean half the effect. By the time that you get up to planet sized bodies, the effect would be so small that other effects on the orbit would likely dominate.
Astroprof’s Page » 99942 Apophis on January 27, 2007 at 12:50 pm: 3
[…] At an estimated 320m across, were Apophis to strike Earth, it would likely strike with an energy of approximately one gigaton of TNT. That is like 1000 hydrogen bombs (note: H-bombs come in many different yields, so it might be only 100 big ones, or 2000 smaller ones). This is about five times larger than the impact that made Barringer Crater in Arizona. But, remember that an actual impact seems unlikely. Still, we don’t really know what asteroid orbits do. The Yarkovsky Effect has an annoying tendency to shift the orbits around a bit, and as critical as even a slight shift is to the computations, that means some unavoidable uncertaintly. So, we will keep watching this one. […]
Astroprof’s Page » How YORP Works on March 9, 2007 at 12:22 am: 4
[…] There’s been talk lately about YORP. It even made a major non-science news site. So, what is YORP, and what does it do? Well, YORP is basically an extension of the Yorkovsky Effect that I blogged about back a bit over five months ago. In fact, the “Y” in YORP stands for Yarkovsky. The term YORP is short of Yarkovsky-O’Keefe-Radzievskii-Paddack. […]
Astroprof’s Page » 2008 CT1 on February 7, 2008 at 1:20 pm: 5
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Astroprof’s Page » 2008 EB61 on March 14, 2008 at 10:47 pm: 6
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