How YORP Works
Published on Mar 8, 2007 at 11:45 pm.
3 Comments.
Filed under asteroids, physics.
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.
I’m not going to explain the Yarkovsky effect again here, so if you are not familiar with it, then go back and read my earlier post so that you can follow what I’m saying here. To summarize, though, the Yarkovsky effect is due to the fact that light has momentum. Higher energy light has higher momentum. As a body is heated by absorbing energy from the Sun, it must release this heat as thermal radiation. The hotter it is, the more energy it releases per second, and the more energy that the light radiating away from the body carries. In the classic Yarkovsky effect described in my earlier post, I talked about how this can lead to changes in an asteroid’s orbit. But, a few decades ago, O’Keefe, Radzievskii, and Paddack each suggested that this same effect could lead to changes in an asteroid’s spin, as well.
To understand how the Yarkovsky effect could affect the spin of an asteroid, we need to understand a few things about spin. First of all, the rate of spin, ω, can be altered by a torque, τ (note: I am using the standards symbols here that I use in my physics classes). The greater the torque, the the greater the change in the rate of spin (or angular velocity, as it is technically called). Torque is given by the equation
where F is a force applied to a body, r is the distance the force is applied from the axis of rotation, and φ is the angle between the direction of the force and a line running from the axis of rotation to where the force is applied. Radiation will basically go outward from the surface (it actually goes in other directions, but those directions are symmetric and so their torques cancel out).
For a spherical body, the radiation going outward from the surface is directed in the same direction as a line running from the center of the body to the surface. Thus, the angle φ is zero, and therefore the sine of that angle is zero as well. That means that there is no torque, and so the Yarkovsky effect can not change the spin of the object.
But, for a non-spherical object, then the situation can be different. Consider the case below. The object, such as an asteroid, is a non-regular shape (this is pretty typical of asteroids). The center of mass of the object lies closer to one end than the other. As the body rotates, it will spin about its center of mass.
Now, consider that the line running from the center of mass to the surface does not generally strike the surface perpendicular to the surface, except in certain places. Thus, the angle φ is not zero, and thus there will be non-zero torque due to thermal radiation emitted. Now, combine this with the Yarkovsky effect. As the asteroid spins, it is heated on the side towards the Sun, but cools on the side away from the Sun. Now, consider the drawing above. The asteroid is shown turning counterclockwise, with the Sun on the left of the drawing. The side of the asteroid on the bottom of the drawing is warmer than the side on the top of the drawing. Thus, on the knob sticking out to the right, there is a greater torque trying to spin the asteroid counterclockwise than there is a torque trying to spin it clockwise. So, the spin of the asteroid will increase. This is the basic idea behind the YORP effect.
The YORP effect has been predicted for decades. Serious computer models were used a few years ago to show that it really should behave this way. But, we now have definite evidence from at least two asteroids, 1862 Apollo and 2000 PH5, that their spin rates have changed, presumably as a result of the YORP effect. Now, this isn’t much change, it would seem. For 1862 Apollo, the accumulated effect of 40 years of the YORP effect has only shaved off a couple seconds from its rotational period. But, that is really a lot when you consider, that these asteroids can go for millions or hundreds of millions of years without any other interaction besides the Yarkovsky and YORP effects acting on them.
The effect will be largest for the smallest asteroids, and for the most irregularly shaped ones (which frequently are also the smaller ones). In fact, we find that for larger asteroids, they have pretty much a random distribution of spins. But, for smaller asteroids, there is a preponderance of asteroids with unusually fast spins. It has even been suggetested that this mechanism could lead to asteroids eventually tearing themselves apart if left alone. So, once again, we find the asteroids to be dynamic systems, not just the spare bits of rock that they’ve been thought of so often for so long until recently.
-Astroprof
A Ler…-- Rastos de Luz on March 10, 2007 at 8:34 am: 1
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michael moss on March 13, 2007 at 12:20 pm: 2
Perhaps an unrelated comment–actually a question: does the universe spin? Everything spins–why not & if so, how to see this since we are a part of the system & cannot see anything outside the system to observe spin?
Astroprof on March 13, 2007 at 10:54 pm: 3
Some years back, I saw a paper that suggested that the universe itself may have spin, but I never saw a follow-up (that doesn’t mean that there wasn’t one, just that I didn’t read it in the mountain of research papers out there!). Certainly, I haven’t heard much about this since that earlier paper. As you say, you have to have a creative definition of spin in you are talking about the universe as a whole.