# Stable Orbit for a Newly Discovered Companion

by on April 7, 2011

The Earth is followed around the Sun by several Near Earth Asteroids in what are called ‘horseshoe orbits.’ Have a look at the NASA image below showing the orbital contours of such orbits. You can see the horseshoe shape, so called because the object’s apparent direction changes as seen by a viewer on the Earth. What’s happening is that the gravitational attraction of the Earth is changing the asteroid’s elliptical orbit. Even though the asteroid always orbits the Sun in the same direction, it cycles between catching up with the Earth and falling behind. It’s the relative motion of the object with relation to both the Sun and the Earth that produces the horseshoe effect.

Image: Starting out at point A on the inner ring between L5 and Earth, the satellite is orbiting faster than the Earth. It’s on its way toward passing between the Earth and the Sun. But Earth’s gravity exerts an outward accelerating force, pulling the satellite into a higher orbit which – counter-intuitively – decreases its speed. When the satellite gets to point B, it is traveling at the same speed as Earth. Earth’s gravity is still accelerating the satellite along the orbital path. The satellite moves into a higher orbit. Eventually, at C, the satellite reaches a high enough, slow enough orbit and starts to fall behind Earth. It then spends the next century or more appearing to drift ‘backwards’ around the orbit. Remember that its orbit around the Sun still takes only slightly more than one Earth year and the apparent backwards motion is only relative to the Earth. Eventually the satellite comes around to point D. Earth’s gravity is now reducing the satellite’s orbital velocity, causing it to fall into a lower orbit, which actually speeds up the satellite. This continues until the satellite’s orbit is lower and faster than Earth’s orbit. It begins moving out ahead of the earth. Over the next few centuries it completes its journey back to point A. Image credit: NASA. Caption: Wikipedia.

The most recent addition to the list of objects in horseshoe orbits around the Earth is asteroid 2010 SO16, discovered by the WISE (Wide-field Infrared Survey Explorer) satellite. New work out of Armagh Observatory in Northern Ireland has now determined that, unlike other such objects, 2010 SO16 has been following the Earth on its orbit for at least 250,000 years. Other ‘horseshoe companions’ remain in this configuration for several thousand years before moving on to other orbits. Moreover, 2010 SO16 has an estimated diameter of 200-400 meters, making it easily the largest of the Earth’s horseshoe asteroids.

The object takes 175 years to travel from one end of the horseshoe to the other, in an orbit quite similar to the Earth’s. Apostolos Christou, one of the authors of the paper on this work, calls the asteroid ‘terraphobic,’ and adds “It keeps well away from the Earth. So well, in fact, that it has likely been in this orbit for several hundred thousand years, never coming closer to our planet than 50 times the distance to the Moon.” Which is, in fact, where it is right now, near the end of the horseshoe trailing the Earth.

Christou and colleague David Asher at Armagh went to work on the object’s orbital stability by creating simulations that modeled the behavior of the asteroid for every orbit it could occupy, running the simulations two million years into the past and the future. All the ‘virtual’ asteroids they plugged into this model remained in the horseshoe orbit with respect to the Earth. So 2010 SO16 has been out there for a long time. What we don’t know at this point is its origin.

Three possibilities present themselves. From the paper:

The existence of this long-lived horseshoe raises the twin questions of its origin and whether objects in similar orbits are yet to be found. The object’s Earth-like orbit makes a direct or indirect origin in the main belt an unlikely, although not impossible, proposition… Another plausible source is the Earth-Moon system. Margot & Nicholson (2003) have suggested that 54509 may have originated within the Earth-Moon system. SO16’s current orbit does not provide such a direct dynamical pathway to the Earth-Moon system as in that case, although the situation is likely to change within a timescale of several times 105 yr. A third possibility is that the object originated near the Asteroid-Earth-Sun L4 or L5 equilibrium point as a tadpole librator.

By ‘tadpole librator.’ Christou and Asher mean objects in so-called ‘tadpole orbits’ around the L4 and L5 Lagrangian points. Objects in these orbits do not move as far from the Earth as objects in horseshoe orbits. At the L4 and L5 points 60 degrees ahead of and behind the Earth in its orbit, it is possible that material left over from the formation of the inner planets may remain. Out of this population may have come the asteroids in horseshoe orbits we see today. Finding out more about such a population would require, say the authors, a space-based observatory in a heliocentric orbit inside that of the Earth, a mission we’re unlikely to see mounted any time soon.

But we can continue to study 2010 SO16 from the ground, starting with its color. Christou and Asher are quoted in this Armagh Observatory news release as saying they’re interested in the object’s color as a marker for its origin:

“Colour, a measure of an asteroid’s reflectivity across the electromagnetic spectrum, can tell you a lot about its origin,” they explain. “With this information we can start testing possible origin scenarios with hard data. If it proves to be unique in some way, it may be worth sending a probe to study it up close, and perhaps bring back a sample for laboratory scrutiny.”

The paper is Christou and Asher, “A long-lived horseshoe companion to the Earth,” in press at Monthly Notices of the Royal Astronomical Society (preprint).

Michael April 7, 2011 at 13:04

Strange objects are these, as they orbit empty space – neither around the earth or the sun!

andy April 7, 2011 at 13:25

Depends on what reference frame you use to draw the orbit…

Interstellar Bill April 7, 2011 at 13:53

In an unrefereed paper a decade ago, posted at
http://www.orionsarm.com/fm_store/SpaceRings.pdf
I outlined a concept of the ultimate mega-habitat, the Space Ring, originated by Forrest Bishop of the Foresight Institute , see
http://en.wikipedia.org/wiki/Bishop_Ring_(habitat)

Space Rings have the advantage over planets of maneuverability, a zero gravity well, a single time zone with short radio lag, and high levels of electrical power available for military laser defense.

Space Rings built at Sun-Earth L1 would go to point A, in order to remain in Earth’s vicinity for a while so immigration could continue.
Ditto for L2 to E.

In the horseshoe orbit a Space Ring could receive asteroids for further Ring-building with none of the Earth-danger (however small) associated with bringing asteroids to the much closer L1 and L2 for the building of the first Space Rings. Their numbers could grow to billions before their stellar occulatations would be noticeable. By that time their peoples would far outnumber Earth-Dwellers, but their gravity and blue sky would make their Earth-sympathy continue.

I still have to look up how many micro-gees of halo-orbital maintenance is required at L1 and L2. This would size the ion rockets needed as the Rings mass up during the multi-decade assembly and eco-stocking process.

Space Rings are the road to a Dyson Swarm, except that once the sky ‘closed’ there would be no reason for the open-sky Ring geometry, since you would see nothing but other habitats. The Swarm habs would be conventional O’Neill cylinders.

Something about Swarms I haven’t heard mentioned anywhere is that it that the outer orbital shells would need concentrators, but it’s hard to picture solar-sails more than ten times bigger than a Ring, corresponding to 100x solar concentration. A full Swarm would necessarily be about a half percent leaky to the original sunlight of its star, while its IR signature would be that of low-emissivity solar cells.

Another unmentionable is that giant stars could support much bigger Swarms than solar stars. Most important of all is that the youngest massive stars, with preplanetary discs, will the supreme prize of interstellar colonizers, while planetary systems will be the leftovers, fit only for stragglers. The Galaxy will go dark with the brightest stars dimming first.

The fact that we see no galaxies going dark is proof we’re Alone.

ant6n April 7, 2011 at 14:12

Well, actually they do orbit the sun. They just have their orbit perturbed by the earth.

Malcolm Ramsay April 7, 2011 at 16:17

If we haven’t “cleared our orbit”- does that mean that we’re not a planet according to the IAU definition?

Rob Henry April 7, 2011 at 16:26

I thought that, if Bracewell probes were studying us, they were most likely to do so from L4 or L5. If these horseshoe orbits get so much closer to Earth, it could only be instability that prevents that being the better option. How many >100m such objects could there be, and what is their most stable orbit? From this article you almost get the impression that there could be swarms of full-on O’Neil habitats circling with us without our yet noticing, let alone a few tiny simple probes.

andy April 7, 2011 at 18:13

If we haven’t “cleared our orbit”- does that mean that we’re not a planet according to the IAU definition?

Well yes, but by this point only the tedious pedants and the more fanatical/desperate wing of the “Pluto is a planet” crowd still care. The rest of us either work with the more sensible dynamical criteria that the IAU definition is a poorly-worded approximation of, or use a definition which does not depend on dynamical considerations (apart from the case where the object itself orbits a planet).

Istvan April 8, 2011 at 11:46

I seem to recall being disappointed in an analysis I found somewhere that the delta-v required to reach 3753 Cruithne (another object in a horseshoe orbit similar to that described for 2010 SO16) was fairly high. Is anyone aware of a similar analysis publicly available for 2010 SO16 at this time?

ljk April 8, 2011 at 12:21

Interstellar Bill, did you see this recent Centauri Dreams article here:

http://www.centauri-dreams.org/?p=17357

As for your quote: “The fact that we see no galaxies going dark is proof we’re Alone.”

Have we been observing galaxies long enough and in sufficient quantities to notice if any of them are getting less luminous? I don’t think so. Plus most astronomers aren’t looking for Kardashev Type 3 civilizations and sure as heck would not admit to them as a reason if they did notice a galaxy getting dimmer. NGC 5907 is a spiral galaxy that astronomers claim is optically dim due to a very large number of red dwarf stars, yet fail to explain why more such stellar islands don’t have similar conditions. A star that is brighter in the infrared than optical is one of the signs that it is surrounded by a Dyson Swarm. Just sayin’.

Again, we need to do a lot more astronomical investigation before we can claim we are alone or not. We have barely gotten outside the door of our world and yet somehow we think we know how the whole Universe works and who else may or may not dwell in it with us.

Rob Henry April 8, 2011 at 15:56

Ljk, it was my understanding that there have been many searches for stage III civilisations, the example of Richard Carrigan’s investigation of the whirlpool Galaxy (that was outlined on this site) being only one of the most recent examples. Obviously, it would take thousands of years of observation for us to notice the dimming of a galaxy from previous recordings, so, I feel that Interstellar Bill was referring to the distinctive pattern of light emanating from a galaxy that is half way through such a transformation.

ljk April 8, 2011 at 17:07

To Rob Henry:

I would have to look up the exact number, but “many” SETI projects for Type 2 and 3 civilizations is a relative term. Most SETI programs throughout its 51 years as of today (April 8, 1960 – Project OZMA) are fairly sproadic and mainly been focused in the radio realm at nearby stars in this galaxy. Only recently (starting in the late 1990s) have there been more searches lasting months at a time and looking in the optical and infrared ranges too.

This is due in part to the fact that only very recently have there been astronomical instruments dedicated to the SETI task; before then, SETI researchers had to beg and borrow for even a few hours at a radio telescope from the “regular” astronomers. Add to all this the fact that we have scanned relatively little of the Milky Way galaxy and even less of other galaxies, and you have several very good reasons why I tend to disagree when people say we’ve searched the Universe and haven’t heard a single peep from an alien species.

And yes I know about the SETI program at Ohio State University that ran from 1973 to 1998, when the university decided they could do better with turning the land that the radio telescope sat on into golf courses and condos. They had dedicated volunteers and they were the ones who detected the “Wow!” signal of August, 1977.

Of course note that unlike the mythological image of SETI people wearing headsets and listening to the Cosmos at computer stations for hours on end, the “Wow!” signal was only noticed hours after it happened when someone noted the strong signal on the printout. There was apparently an even stronger candidate detected in Australia in 1990, but I have heard very little about that one (details are appreciated) unlike the OSU find, which has never been found since.

If you want another real example of how searches went back in the day, especially regarding the Type 2 and 3 civs, check out the Keay Davidson biography of the late great Carl Sagan published in 1999. Sagan actually conducted a search for beings from the Andromeda galaxy (Messier 31) in 1975 at Arecibo Observatory. He sat at a control panel for several hours, which apparently got rather boring, and then stopped. I think it is safe to say that with Andromeda being almost 3 million light years away, that listening for a chance radio signal that could make it across all that intergalactic space for a couple of hours is not exactly an extensive determination if anyone is home there or not.

I am not saying all this to be mean to anyone, I am just pointing out that real SETI, especially until just over a decade ago, was usually not what most people think it is. This is why I am both glad to see that some institutions are finally getting serious, dedicated, and expansive about the search, and why people REALLY need to understand that at best what most of our SETI efforts have concluded is that apparently there is no one in the galaxy (or any other) broadcasting loud and long at us at least since we have had the capability, will, and understanding to find such transmissions.

Eniac April 8, 2011 at 22:57

The fact that we see no galaxies going dark is proof we’re Alone.

Proof? Hardly. We could be surrounded by civilizations who do not build Dyson swarms or Dyson anything. Why not? Dyson things are cool ideas, but elevate them to a necessary consequence of intelligent life? I don’t think so.

There are so many different ways to imagine the future that the idea that any one of them is so inevitable as to serve as the basis of a “proof” is ludicrous.

Rob Henry April 9, 2011 at 21:42

Ljk, thanks for alerting me as to the flimsy nature of some of these searches for stage II or III civilizations, though I was of the opinion that rather more of the earlier ones were done in the old communist block than in the West. One the greatest dangers to all science occur when everyone starts to assume the evidence against a theory is stronger than it is, so this point of yours is particularly poignant.

Not quite so many thanks for your implicit acknowledgement of those of us who live in the southern hemisphere, by giving the Andromeda Galaxy its Messier catalogue number, just in case it was too obscure for us to have heard of by name. We have the wonderful Magellanic Clouds (no Messier catalogue number, so you will just have to believe me), and many in this ‘lesser half” of the world have seen a supernova with their own eyes… so there!

Andrew W April 10, 2011 at 2:25

Istvan,
SO16 is number 4437 on this list.
http://echo.jpl.nasa.gov/~lance/delta_v/delta_v.rendezvous.html

Andrew W April 10, 2011 at 2:48

If you’re looking for a NEO with low delta-v from the earth system, 2011CG2 is promising, according to Near Earth Objects – Dynamic Site, it’s diameter is 150-350 metres.

ljk April 11, 2011 at 2:48

Well, Rob Henry, I didn’t think I was making any kind of a swipe at the Southern Hemisphere nor its view of the sky, which I have heard is quite spectacular. I never thought mentioning a Messier object (and I was doing so out of thoroughness) could somehow become offensive.

andy April 12, 2011 at 18:41

Dyson spheres always struck me as being highly implausible: you first have to deconstruct a planetary system, then launch vast amounts of material into high-inclination orbits. This requires a huge amount of energy to do. After you’ve built it, you then have to prevent the various components of the sphere crashing into each other which would result in everything collapsing onto the star (if the sphere has no net angular momentum) or into a ring. Solid Dyson spheres are impossible because you’d essentially need the strong force to work on macroscopic scales, which it doesn’t. A sphere would also be unstable: any displacement of the sphere with respect to the star will result in forces that act to increase the displacement.

Yes these things would present nice observational signatures, which is presumably why the SETI types give them so much attention, but there doesn’t seem to be a particularly convincing case for why we should expect anyone to build one. Big Dumb Objects and all that…

Rob Henry April 12, 2011 at 23:52

Andy, you are the latest in a long line to claim that solid Dyson spheres need to be built of non-atomic material, but I must be missing something because I don’t see it. Dyson spheres have no gravity on their insides, so the population inside must live on fast and vast low friction ‘trains’ that race around the inside of the sphere and generate large centrifugal forces against those spheres, and these would be made to balance the gravitational centripetal force. The flexing forces generated by the varying opposition of these two forces with time will be vast, but I don’t see the proof that they would need non-molecular materials for their integrity, let alone the strong nuclear force!

ljk April 13, 2011 at 13:28

The main point as to why anyone would build a Dyson Shell that people keep missing is the sheer incredible coolness factor of having one. Five billion Earths in terms of land area for a solid (Type 2) version!

But remember, Dyson Shells do not have to be solid spheres, nor is that what Freeman Dyson envisioned back in 1959. Swarms of large colonies around a star would work. And look up the concept of the Matroishka Brain for versions that are not meant as habitats for organic creatures such as ourselves, which actually makes even more sense.

Eniac April 13, 2011 at 13:33

Rob: Let’s think about those ‘trains’ a little. The Earth’s orbital velocity is 30 km/s, its centripetal acceleration is 0.006 m/s^2. To get 1 g of artificial gravity (~10 m/s^2) for the train riders, the trains would need to move at 30*10/0.006 ~ 50,000 km/s, or 1/6th of the speed of light.

That, or the strong force material.You pick….

The good part about this is interstellar travel is real easy: Just exit the sphere at the right point. The hard part is getting on or off the train…

Rob Henry April 13, 2011 at 16:40

Eniac, good point, but as you probably realise by now, you forgot to square root your differential factor. Also I would cook in perpetual midday tropical sun. Using a more survivable diameter of twice Earths orbit and rooting the factor I find I need ‘just’ 1,700km/s

ljk April 18, 2011 at 10:17

I want to clarify something about the basic nature and history of SETI that I think has been misinterpreted and lost over the decades, or perhaps never publicly updated strongly enough by the so-called mainstream SETI groups.

When the modern search for alien intelligences was first conceived and executed over half a century ago, it was thought that perhaps there were already many advanced civilizations communicating with each other across the Milky Way galaxy and we were only now just capable of tuning in to those broadcasts with our radio telescopes – radio astronomy being a fairly new discipline at the time. This is why folks like Frank Drake assumed they could just aim a dish at some nearby Sol-type stars and pick up the extraterrestrial equivalent of I Love Lucy and the latest addition to the Encyclopaedia Galactica in short order, as he did with Project Ozma in 1960.

It took a while for the SETI groups to realize that finding others in the Cosmos would not be as easy as they predicted, though the combination of the mainly sporadic search efforts and the belief that they just needed to tune into more radio channels added to the years of SETI’s attitude that there were plenty of other beings out there and we would find them if we just got sophisticated enough.

In a sense that may still be true, but most mainstream SETI professionals now think that advanced societies may be much farther away and are not making a major effort to communicate with less sophisticated species such as humanity. Certainly there has been nothing of an artificial alien nature terribly obvious yet seen or heard by SETI.

Of course the concepts of laser and infrared transmissions, major astroengineering projects visible to Earth, and even probes quietly observing us from within our own Sol system are finally starting to make some headway in the SETI field, but the general public and even professional traditional image of a group of dedicated astronomers listening for radio signals from an alien planet not very different from us has yet to be fully updated to reflect the true state of SETI, astrobiology, and exoplanet data and studies in the early 21st Century.

hiro April 20, 2011 at 15:28

Why don’t we choose this object as the target for the asteroid mission in 2020s?

Mephane July 11, 2011 at 7:32

“The fact that we see no galaxies going dark is proof we’re Alone.”

Another thing to add what has been replied to this claim:

The universe is vast. Even the closest galaxies’ distances can be measured in millions of lightyears. This means in order to be able to detect significant effect from a type 3 civilization on a galaxy, that civilization would have to be
a) interested in doing such large scale engineering
b) physically able to do so (just because they have the energy of a galaxy does not mean there are no limits on what they can do with the galaxy)
c) old enough so that their construction could have started early enough so that the light showing their effects would reach us now, which means millions to billions of years ago.

And basically, we have no idea about any of those 3 issues, just vague speculation. This is not a good basis to claim “this is proof we are alone”.

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