Two More Co-Orbitals of Earth
Published on Jan 27, 2009 at 4:25 pm.
14 Comments.
Filed under Earth, asteroids, astronomy.
In my last post, I wrote about the asteroid 2009 BD, which has an orbit very nearly that of Earth’s. But, it is not Earth’s only orbital companion. I know of more than a half dozen asteroids whose orbits would be considered co-orbital with Earth. The two that I want to talk about today have even stranger orbital properties. These are the asteroids 2002 AA29 and 2003 YN107.
As with 2009 BD, these asteroids have an orbit almost the same as that of Earth, but not quite. Both have orbits that are a bit inclined with respect to Earth’s orbit, as you can see in the accompanying orbital diagrams. These diagrams, courtesy JPL’s Small Body Database, show an oblique view of the Solar System, so you can see how the orbits drift above and below Earth’s orbit. They also have orbits nearly as elliptical as Earth’s, but the long axes of their orbits is not aligned with that of Earth’s orbit. Thus, they drift closer and farther from the Sun that Earth. This drifting closer and farther while going up and down (compared with the plane of Earth’s orbit) makes their orbit appear almost helical if you were to look at the orbit from Earth’s perspective instead of from the Sun’s point of view. Paul Wiegert has a nice explanation of this sort of orbit, and I’m using a couple of his images here, including this one:
This is a typical orbit for this sort of asteroid, as seen from Earth. Furthermore, it is also what we call a horseshoe orbit. The name comes from the fact that typically, if the asteroid is moving a little faster than Earth, when it approaches from behind in Earth’s orbit, Earth’s gravity pulls on it a bit, it speeds up, slides to an orbit just a shade farther out than Earth’s, slows down, and Earth pulls away from it. Effectively, it would look like the asteroid got close to Earth in its helical orbit and then started going back the other way. Eventually, Earth catches up with it again, and the reverse happens. So, the asteroid simply goes back and forth along paths that loop in and out of Earth’s orbit, and whenever it gets close to Earth, the orbit of the asteroid shifts ever so slightly so that it continues to loop in and out of Earth’s orbit for years, decades, or centuries until it comes close to Earth again. One of the first asteroids that I heard about that does this sort of thing was 3753 Cruithne, discovered in 1986. Clearly, these orbits are of bodies about the Sun, but they are greatly influenced by the presence of Earth and Earth’s gravity. But, there are plenty of other bodies in the Solar System influencing these bodies, and in order for them to behave as they do, they have to have an orbit that is unaltered by these other bodies. That isn’t going to happen. Thus, these orbits, while pretty stable for a long time, are ultimately unstable. For most unstable orbits, that means that they can be shifted into an orbit that either comes too close to Earth at some point, resulting in their being thrown out of this neat orbital relationship with Earth. They can even wind up on a path that would ultimate collide with our planet, though that is far less likely than their being tossed into another orbit.
But, one really interesting thing that can happen is if one of these asteroids approaches Earth at just the right spot in its orbit. Then, their orbit becomes even more tightly entwined with Earth’s. In this case, they orbit the Sun always in the vicinity of Earth. If you were looking at the asteroid from Earth, it would look almost as if the asteroid were spiraling around Earth. This would be a case of an asteroid whose orbit, instead of going back and forth in the helical horseshoe orbit above, would be trapped in the gap in the horseshoe shape shown. Such an orbit would look like the following (also from Wiegert):
For a while, Earth would be orbiting the Sun with a companion. It is important to note that, while the asteroid looks like it is looping around Earth, it is in fact still orbiting the Sun, not Earth. That means that it is not really a satellite, or moon, of Earth. It is still a sun-orbiting body, but its orbit looks almost like that of an Earth satellite body, so we sometimes call it a quasi-satellite or a quasi-moon. The asteroid 2003 YN107 got trapped in just such a situation a few years back. For about ten years, from 1996 to 2006, it made loops around Earth, taking one year to make one complete circuit. It is small and wasn’t discovered until 2003, having already been a temporary companion of Earth for ten years. In 2006, though, it managed to get a slight nudge to get back into its normal horseshoe orbit.
2002 AA29 does something similar. It orbits the Sun. But, its orbit looks like the horseshoe seen above. About once per century it approaches Earth, where it is turned back. Eventually, it approaches from the other side (one time it is gaining on Earth, and the next Earth gains on it). Again, it is turned away. It bounces back and forth, gaining on Earth, then losing ground until Earth catches it. It, then, pulls away once again. But, once in a while it gets caught into a temporary holding pattern, spiraling around Earth. That last happened perhaps nearly 1500 years ago, and it may happen again in about 600 years. There are other asteroids with this behavior, too.
So, Earth does not orbit the Sun alone. Besides our Moon, there are a variety of other bodies out there keeping us company.
-Astroprof
Orbit diagrams credit: JPL Solar System Dynamics, Paul Wiegert’s 2002 AA29 page
Mang on January 28, 2009 at 7:04 am: 1
It would be interesting to hear about the others!
I was reading somewhere that Cruithne wasn’t truly coorbital that it was too eliptical and onclined. It seems like a narrower definition of coorbital than I’d heard before.
If one of these had been more obviously visible, wouldn’t that have baked a few peoples brains back before modern astronomy.
Surprisingly there is no wikipedia article on Earth Coorbital Moons/asteroids.
Mang on January 28, 2009 at 7:17 am: 2
Woops onclined = inclined.
Astroprof on January 28, 2009 at 12:14 pm: 3
I’ve also heard debate on whether or not Cruithne should be considered co-orbital. I have heard at least one person suggest that it is closer to being an Earth Trojan than the other co-orbitals, but in my book that also makes it co-orbital. Since it’s orbit is so tied to Earth’s, though, I figure that it should count. As with many things, the universe is quite vast, and there are a lot of things in it. Whenever you get a definition of something that has some give to it, there is apt to be something out there that is on the edge of that definition.
Week of January 26th, 2009 « Dad2059’s Webzine of Science Fiction, Science Fact and Esoterica on January 28, 2009 at 1:54 pm: 4
[…] Co-orbitals of Earth […]
Ed Davies on January 28, 2009 at 5:33 pm: 5
I read somewhere, and my amateur back of the envelope calculations confirmed, that “Earth’s” moon could also be considered co-orbital in the sense that throughout its orbits (monthly and yearly) the Sun has more gravitational influence on it than the Earth. Any comments?
Tony Dunn on January 29, 2009 at 8:10 pm: 6
Very interesting blog!
I don’t think the debate about Cruithne isn’t about whether or not Cruithne should be considered co-orbital. It is definately in a librating, co-orbital horsheshoe orbit with Earth. The debate is about whether or not Cruithne should be considered “Earth’s 2nd moon”. I vote no!
Maybe I’m misunderstanding what co-orbital means. Can anyone clear it up. I’ve been under the impression that co-orbital means the object is in a 1:1 resonance with Earth. There are 5 types of 1:1 resonances:
Trojan
Tadpole
Horseshoe
Quasi
Direct orbit
Based on my definition, 2002 AA29, Cruithne, and 2003 YN107 are co-orbitals of Earth. But 2009 BD is not co-orbital. 2009 BD simply has an orbit whose semi-major axis, and hence period, is very close to Earth’s. But it is not a trojan or tadpole. After departing from Earth’s vicinity, it will round the L3 and approach us from the other side, like a horseshoe. But unlike a horseshoe, Earth will not repel it in a rotating frame. It is currently closest to a quasi orbit, but fails to get trapped into one. With the exception of direct orbits, objects that come too close to Earth can’t be co-orbital, as Earth will heavily perturb them, significantly altering their semi-major axes and hence their periods.
Here are some diagrams I made of 2009 BD9’s trajectory based on its nominal data. Both diagrams are in a rotating frame of reference. The first shows its path near Earth during its current visit. The 2nd shows its path around the sun:
http://orbitsimulator.com/gravity/images/2009BD_2.GIF
http://orbitsimulator.com/gravity/images/2009BD.GIF
Here’s some examples of each type of co-orbital asteroid (assuming I got the definition of co-orbital correct:) :
Direct Orbit:
Earth’s moon directly orbits Earth and may therefore be considered co-orbital.
Asteroid 2006 RH120 was temporairly captured into a direct orbit a few years back. It orbited Earth for over a year, so Earth temporarily had another moon. Here’s 2 diagrams of its orbit around Earth. The first is top down, and the 2nd from the ecliptic plane. Also visible is the orbit of the moon:
http://orbitsimulator.com/gravity/images/newMoon1.GIF
http://orbitsimulator.com/gravity/images/newMoon2.GIF
Trojan:
Here’s an animation of Mars’ known trojans: http://www.orbitsimulator.com/gravity/articles/eureka.html
Here’s a diagram of Jupiter’s Trojan and Greek Asteroids: http://www.orbitsimulator.com/gravity/articles/jupitertrojans.html
A tadpole is simply an elongated trojan. Here’s an image of some hypothetical tadpoles, on my page that explains about rotating frames:
http://www.orbitsimulator.com/gravity/tutorials/rotatingframe.html
Horseshoe:
Here’s an animation of Cruithne in its horseshoe orbit: http://www.orbitsimulator.com/gravity/acruithne.GIF
Here’s some diagrams of 2002 AA29’s orbit: http://www.orbitsimulator.com/gravity/articles/2002aa29.html
Quasi
Here’s an animation of 2004 GU9 in a rotating frame, showing its quasi orbit with Earth: http://orbitsimulator.com/gravity/images/2004gu9.GIF
I believe 2004 GU9 has left its quasi-state for the moment. Usually objects that leave a quasi state enter horseshoe orbits. I believe Earth has another longer-lasting quasi at the moment. I’ll look it up if anyone’s interested.
I think there’s a few asteroids I’ve left off this list too.
In addition to co-orbitals (1:1 resonance) its possible for Earth to have other resonances with asteroids. They’re likely to be near 1:1, such as 4:5, rather than resonances like 3:1, since such an orbit would have to be elliptical enough to make it a Mars or Venus crosser.
Here’s a list of some resonant asteroids, with graphs and animations. Keep in mind that I only plotted their nominal trajectories, so they might not actually be resonant if their true position and their expected position differ greatly. The one I label as a Jupiter horseshoe had its nominal position updated, and is no longer considered horseshoe.
http://orbitsimulator.com/astr699/ERS.html
Another interesting thing about horseshoe and quasi asteroids is that they are always short-lived. For example, if I simulate Cruithne out a few thousand years, it escapes from its horseshoe orbit, while other asteroids get captured into one.
Tony Dunn on January 30, 2009 at 11:51 am: 7
How come my comments never appear?
Tony Dunn on January 30, 2009 at 11:53 am: 8
ok, this one appeared, but the last 2 times I tried to post to this blog, the comments didn’t appear, and when I tried to repost, it told me “oops, looks like you already said that”
Astroprof on January 30, 2009 at 3:35 pm: 9
Tony, I’m with you. While there may be some debate as to what co-orbital means, I think that all of these are co-orbitals.
Oh, and I resurrected your earlier comment from the spam filter. You had a number of hyperlinks in it, and since many spam comments have lots of hyperlinks, it filters those comments out, and sometimes other comments from the same person. With it catching several hundred comments per day as spam, a few legitimate ones get caught by accident. Sorry.
Astroprof on January 30, 2009 at 4:19 pm: 10
Ed, I seem to remember many, many years ago that Isaac Asimov once argued that the Moon and Earth were like a double planet, each orbiting the Sun in wiggly paths distorted by the other’s gravity. At no time does the Moon actually go backward in its path around the Sun. It merely speeds up and slows down as it wiggles. That may be pushing it as far as co-orbitalbility (new word there!), but this is yet another instance in which things are bit more complicated than they appear, and the language and terminology hasn’t kept up.
SupplementAndNutrition on February 3, 2009 at 9:34 am: 11
Great post, a lot of info thanks!
Astroprof’s Page » Defining Planets (Part II) on February 4, 2009 at 11:45 am: 12
[…] doing that. This is much the same concept as Cruithne and Earth’s orbital relationship, or Earth’s co-orbital asteroids. Now, that is something that people often latch onto as a reason to say that Pluto is not a planet. […]
Astroprof’s Page » Defining Planets (Part IX) on March 3, 2009 at 4:40 pm: 13
[…] about the asteroid 2009 BD, which has nearly the same orbit as Earth. I followed up that posting with one about other Earth co-orbital asteroids. That raised the whole question about the definition of a […]
Link list – 28th January 2009 | Astronomy Link List on April 6, 2009 at 9:58 am: 14
[…] Dreams The inner solar system is a very crowded place as this report from Centauri Dreams explains. Two More Co-Orbitals of Earth Astroprof’s Page 2009 BD is not the only NEO which orbits along with the Earth, 2002 AA29 and […]