The Kirkwood Gaps
Published on Mar 17, 2008 at 8:13 pm.
7 Comments.
Filed under asteroids.
In my last post, I mentioned that the newly discovered asteroid 2008 EB61 is located near one of the Kirkwood gaps. So, today, I thought that I’d say a bit more about the Kirkwood gaps.
The gaps are not really gaps in the asteroid belt, but they appear to be when a histogram of the asteroids is plotted in a certain manner. Asteroids orbit the Sun in elliptical orbits. Some of the orbits are far more elliptical than others. If you simply plot the positions of asteroids, then the asteroid belt looks pretty much continuous. However, if you plot the distribution of asteroids as a function of their semimajor axes, then something interesting shows up. (The semimajor axis of an orbit is sort of like the average distance from the Sun. I wrote about orbits a little over a year ago. You can read that posting for more information about orbits and the semimajor axis of an orbit.) Plotted in this way, you see that certain semimajor axes don’t have very many asteroids in them. Here is such a plot from the IAU’s Minor Planet Center:
You can see that there appear to be “gaps” in the distribution of asteroids. The first person to observe this was the astronomer Daniel Kirkwood in 1866. That is why they are called Kirkwood gaps. Furthermore, Kirkwood noticed that these gaps were not arbitrary. Each one corresponded to a distance from the Sun at which a body would have an orbital period that was commensurate with Jupiter’s orbital period. That is, the orbital period of the asteroid and the orbital period of Jupiter could be expressed as a ratio of rational numbers. For example, the 2:1 gap meant that the asteroid would orbit exactly twice each time that Jupiter orbited once. The 7:3 gap occurred where the asteroid orbited the Sun exactly 7 times for every three times that Jupiter orbited. Other gaps occur at the 5:2, 4:1, 8:3, 7:2, 5:3, 10:3, etc positions. Some of the gaps are stronger and more noticeable, but at each of these positions, there are fewer asteroids to be found. Interestingly, those asteroid that are in the gaps tend to have very elliptical orbits.
Since the gaps are associated with an orbital resonance with Jupiter, Kirkwood correctly assumed that Jupiter was the culprit. His explanation, though, was slightly off. Kirkwood believed that Jupiter was simply pulling on the asteroids and pulling them out of orbits that were commensurate with Jupiter’s. However, a few decades ago, when powerful and fast enough computers were available, we learned that Kirkwood’s explanation may have been a little too simple. By using computer simulations of Jupiter, the Sun, and asteroids, astronomers were able to show that an orbit in one of the Kirkwood gaps doesn’t just drift out of the gap due to Jupiter’s influence. Rather, the repeated tug that Jupiter makes on the asteroids in the same part of the asteroids’ orbits over and over again can alter the orbit in ways that Kirkwood could not have known. Rather than simply moving the asteroid, Jupiter’s influence is to make the asteroid orbits more elliptical. The eccentricity of the orbit (how elliptical it is) gets larger in a chaotic manner. That means that it is not something that we can predict. The asteroid then begins to follow a path that is more and more perturbed until either it passes too close to one of the planets and is hurled out of its orbit, or else it simply runs into one of the planets. Either scenario depletes the population of asteroids with that semimajor axis. That is not believed to be the likely origin of the gaps.
This is a chaotic change in semimajor axis. It doesn’t just happen all at once, but once it gets going, it can go quickly. So, asteroids can orbit in an orbit commensurate with Jupiter for millions, even billions of years before they are shifted into such elliptical orbits. So, the gaps are not depleted all at once. And, the exact nature of the orbital resonance can also determine how likely the orbit is to be shifted. That can explain why some of the gaps are less empty than others. But, as I have indicated before, asteroids do move around. So, asteroids whose orbits are near those of the Kirkwood gaps can drift into those gaps, and then eventually be tossed around the Solar System.
Such an understanding of orbits also explains why there has been a more or less steady rate of asteroid bombardments of the inner planets. Originally, the idea had been that the asteroids running into the inner planets were simply leftovers from the formation of those planets. No doubt that is partly true. But, some of the asteroids now flying through the inner Solar System also were likely once in the asteroid belt and were shifted out of their orbits somehow. The most likely way for them to be shifted out of the asteroid belt is for Jupiter to nudge asteroids in the Kirkwood gaps into highly elliptical orbits that carry the asteroids far from the asteroid belt.
But, you don’t have to worry about the newly discovered asteroid. It is not likely to be doing that in the near future, or even the not-so-near future. If it ever does drift into a Kirkwood gap and is moved into such an elliptical orbit that it might threaten Earth, then that would likely happen long after we are all gone and Earth is no longer even habitable to our species.
Oh, and I should also mention that the graphic above is a plot of over a hundred thousand bodies. Kirkwood figured out the gaps with fewer than 100 asteroids. That is truly remarkable.
-Astroprof
Ed Minchau on March 17, 2008 at 11:32 pm: 1
I would be very interested to see a three-dimensional plot of semimajor axis vs. semiminor axis (or equivalently, eccentricity) vs. distribution.
Tony Dunn on March 27, 2008 at 3:15 pm: 2
Any idea why the 3:2 resonance is overpopulated?
BC on March 28, 2008 at 1:43 pm: 3
“If you simply plot the positions of asteroids, then the asteroid belt looks pretty much continuous.”
Not quite true. I am currently working on a 3D viz of the asteroid belt and you can most definitely identify the 4:1, 3:1, 5:2, 7:3, and 2:1 by eye. The 5:2 and 7:3 are hard to distinguish from each other, being at 2.82 and 2.95 AU respectively.
Astroprof on March 28, 2008 at 2:08 pm: 4
Tony, the Hilda asteroids that populate the 3:2 resonance are an interesting case, and I\\\’ll be blogging about them at some future date.
BC, it depends on how you plot things. If you grossly plot the inner solar system in two dimensions, as done here (http://cfa-www.harvard.edu/iau/lists/InnerPlot.html)
then you don\\\’t see the Kirkwood gaps.
BC on March 28, 2008 at 3:56 pm: 5
I suppose it all depends on the point size for an asteroid vs resolution.
Either way, I’m always fascinated by orbital resonances, in particular, Io-Europa-Ganymede is my favorite.
Tony Dunn on March 29, 2008 at 8:42 pm: 6
Io, Europa, and Ganymede are facinating because their orbits are very round, yet the resonances would not exist without the small bit of eccentricity that exists. And that small bit of eccentricity is also responsible for the tidal heating that gives Io its volcanos, Europa, and possibly Ganymede their subsurface oceans. And I think one of the inner moons is also part of this resonance, for a 4:3:2:1?? I believe that they’re slowly spiraling outward, while remaining in lock step, and one day Callisto may be captured into this resonance as well.
I’ll look forward to the blog on the Hildas. I’ve got my own ideas, and I’m currently running simulations to try to confirm what I suspect (although it’s quite possible that others have already figured this out). The Hildas are locked in a 3:2 mean motion resonance, which protects them from runaway eccentricity jumps. Most of the asteroids in 3:1, 5:2 and 4:1 zones are not in a mean motion resonance, rather they just coincidentally have their sma’s there. If their orbits were more eccentric, the aphelions would be closer to Jupiter, and they could be locked into a mean motion resonance, like Toutatis. However, eccentricity great enough to do this also makes them Mars and/or Earth-crossers, so they’re not long-lived in this configuration. A close passage with Mars or Earth alters their sma’s enough to get them out of these resonant zones. If my sims are successful at demonstrating this, I’ll make a report on my web site.
Astroprof’s Page » 2008 BT18 Passing Earth on July 13, 2008 at 1:15 pm: 7
[…] the orbit of 2008 BT18 has a semimajor axis that is very close to one of the asteroid belt’s Kirkwood gaps. That may have something to do with its large […]