Earth’s Traveling Companion

There's something deeply intriguing about the interplanetary objects known as Trojan asteroids.

The great French dynamicist Joseph-Louis Lagrange predicted in 1772 that small bodies might be sharing Jupiter's orbit, in gravitationally stable sweet spots (now called Lagrange points) located ahead of and behind the planet by 60°. But it wasn't until 1906 that the first of these, 588 Achilles, was spotted. Today more than 4,800 Jupiter Trojans are known, with roughly two-thirds in the preceding "Greek camp" (L4) and a third in the trailing "Trojan camp" (L5).

Earth's Trojan asteroid
Not much to look at, the asteroid 2010 TK7 nonetheless represents Earth's first Trojan asteoid. NASA's WISE spacecraft captured the view at top in October 2010 at the infrared wavelength of 4 microns. Then, in April 2011, a follow-up image was recorded by the Canada-France-Hawaii Telescope in Hawaii.
M. Connors & P. Wiegert (top); C. Veillet (bottom)
Within the past two decades, astronomers have found four Trojan asteroids sharing the orbit of Mars and seven accompanying Neptune. They've looked for companions to Earth as well, but the geometry is all wrong: Earth's Trojans would spend most of their time in the daylight sky.

But the odds tipped back in observers' favor with the 2009 launch of NASA's Wide-field Infrared Survey Explorer (WISE), which recorded big swaths of sky 90° away from the Sun. Late last year, Canadian astronomers Martin Connors (Athabasca University) and Paul Wiegert (University of Western Ontario) picked through the spacecraft's scans and identified one object, designated 2010 TK7, that seemed to have an Earthlike orbit. Follow-up was needed, but that wasn't possible until this past April, when it was swept up by two observers in Hawaii.

Their suspicions confirmed, Connors, Wiegert, and Christian Veillet (Canada-France-Hawaii Telescope) report the discovery in July 28th's Nature.

This little body is tied to Earth's preceding Lagrange point. But if you're imagining it circling the Sun in lock step with our planet, think again. The orbit of 2010 TK7 is distinctly eccentric (0.19) and inclined (21°). In fact, it's never actually at L4. Instead, it vacillates widely — almost wildly — in a 400-year-long epicyclic pattern that at times brings it relatively near Earth (though still many times the Moon's distance) and at others places it on the far side of the Sun from us, near the L3 point.

Orbit of asteroid 2010 TK<sub>7</sub>
The small asteroid designated 2010 TK7 is locked in an orbital resonance with Earth. This plot shows the range of separation between the asteroid and our planet over a 400-year period. The red line is its average orbit, which is pinned to the L4 Lagrange point that precedes Earth by 60°.
M. Connors & others / Nature
In fact, its motion is a little hard to fathom in a static representation. So Wiegert has cooked up some very instructive animations to help us all out. A 10-MB Windows .avi file is here, and a 7-MB Quicktime .mov version is here. (He's got some other nice graphics and details about 2010 TK7 on this website.)

Earth's little buddy is so wide ranging that it might even occasionally spend some time resonating around the distant L3 point. In fact, gravitational influences from Jupiter make the orbit chaotic, and there's no way to know with certainty where 2010 TK7 was or will be when its orbit is tracked for more than 10,000 years.

Unfortunately, even though Earth probably has other Trojans in its entourage, WISE won't be able to see them. The spacecraft ran out of its cryogenic coolant last October, and on February 17th principal investigator Ned Wright sent a command to turn off WISE's transmitter for good. Word is that the spacecraft will remain in hibernation, awaiting a possible wake-up call in the future.

15 thoughts on “Earth’s Traveling Companion

  1. R. Carroll

    Since this asteroid matches Earth’s orbit to some degree, would it require relatively low energy to reach? Perhaps it could be a candidate for astronaut visits.

  2. Kelly BeattyKelly Beatty

    Richard: good question! you would think this little body would be relatively easy to visit. but the discoverers calculate that the large inclination actually makes it harder to reach than many near-Earth asteroids.

  3. Dan

    So does that mean, according to the 2006 revised definition of a planet, the Earth is not a planet because it has not cleared its "neighborhood"? :-)

  4. J Zander

    This crossed my mind too. I think we need to go back and fix, er -cough, cough, delete, cough- that whole ‘cleared the neighborhood’ phrase.

  5. Rich Zitola

    I too am really surprised it would be so hard to visit. I don’t quite understand why inclination is such a problem when you can just use a lunar gravity assist a la Ulysses. I guess that might require passing *through* the Moon, which as you know, is rather inconvenient.

  6. Rich Zitola

    So this has got me reading up on orbital mechanics once again. Have a look at this GREAT article:
    http://ccar.colorado.edu/asen5519/cma/documents/ASPapercosIOK.pdf
    which says "A single lunar swingby on a translunar trajectory that barely gets to the moon can add sufficient
    energy that the spacecraft escapes the Earth-Moon system."
    If that’s true, and presuming that any orbit about L4 has roughly the same Sun-relative energy as the Earth’s orbit, then again, shouldn’t the minimum energy to get to this trojan be not much more than the minimum energy to get to the Moon? C’mon Kelly, where’s our resident orbit designer? :)

  7. Kelly BeattyKelly Beatty

    Rich: the problem is that 2010 TK7 is never actually *at* L4. it’s looping up and down, in and out, around it. so if you design a mission to intercept 2010 TK7 when it’s in Earth’s orbit plane, at that moment the asteroid itself is moving quickly up or down. it’s not enough just to meet up with it — you need to match its velocity too.

  8. Rich Zitola

    Good point. I knew that it wasn’t necessary for objects to be specifically at L4, but I had no idea the region of stability around L4 was so huge. That animation you linked to is fascinating, though I think still a little misleading because of the rotating reference frame. It gives the impression that TK7 is madly rushing around those loops when in fact that motion is extremely slow compared to the sun-relative orbital motion of both bodies. If they had included the celestial sphere instead of that digital year-counter, the stars would be whizzing around so fast it would just make you dizzy.

  9. Randall Osczevski

    In her 1954 fiction book for children, "The Wonderful Flight to the Mushroom Planet", Eleanor Cameron envisioned a small companion world sharing Earth’s orbit. This tiny world could only be seen through a telescope fitted with a special "stroboscopic filter". As described, this device sounds suspiciously like a speckle interferometer, however, stellar speckle interferometry was not invented until nearly 20 years later. Perhaps the next one astronomers find will be green.

    Randall Osczevski

    [Detecting Planets in Binary Systems with Speckle Interferometry SIMON P. WORDEN http://history.nasa.gov/CP-2156/ch2.10.htm

  10. Giovanni Rastelli

    J. L. Lagrange was not french but italian, as born in Torino in 1736. In 1766 he moved to Berlin and in 1787 to Paris. As many italian scientists, in his times as today, Lagrange had to search abroad for a better career. The same did before him the astronomer Cassini and the musician Lulli (Lully). For several interesting facts about Lagrange’s life and work see the well done wikipedia’s site.

    http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange

  11. Michael C. Emmert

    I’ve done a bunch of simulations of this very scenario on GravitySimulator. I think the dwarf planet Eris formed in the Sun/Neptune L4 (or it’s mirror L5) and spent a lot of time on that. I actually never did Earth. My bad.

    Anyway, Ed Belbruno asked me how Eris got such a wild 44 degree inclination and I found that encounters with Neptune wouldn’t do the job. The best I could do was about 30 degrees, after that Neptune encounters would more likely put the Lagrangoid back in the invarient plane. I was on the verge of discovering the Kozai mechanism when I ran across it accidentally while googling something else (eCosi = k, where e is eccentricity, i is inclination, and k is a constant for that system. eCosi is a conserved quantity).

    My simulations confirm those attached to this article.

    I’m sure the authors of this article are ecstatic that some idiot got the same result :D

  12. Frank ReedFER

    Well, you know, Lagrange never signed his name in the Italian form "Giuseppe", instead always in the French version. And French and Italian were both widely spoken in Piedmont at the time, French more so in the upper class circles. The issue seems to have become important to some people in the 19th century when European nationalism really took off. If you go to Google Books Advanced Search page and search for pages with "Lagrange" and "Italian" in the year 1860, you’ll find an article by a Mr. "De Morgan" discussing the matter. But in the period when Lagrange lived, many scientists really did not count themselves as members of particular nationalities. They were trans-national. That was one of the great benefits of the Enlightenment. My personal favorite on this score is the mathematician/astronomer "Baron de Zach" or "Baron von Zach", depending on where and when he was writing, who lived and worked in Germany, Piedmont (Italy), and then France. He published in German, French (while living in Piedmont), and English. But he was born in modern Hungary and many modern nationalists therefore claim him as Hungarian. Go figure. Amusingly, the Baron de Zach once wrote a rather long article speculating on the nationality of Copernicus: was he Polish or German? His conclusion — German. Naturally.

  13. Frank ReedFER

    For Dan: actually, this is exactly what the dynamicists were talking about. The Trojan asteroids in the orbit of Jupiter were obviously well-known to them when they were discussing the "demotion" of Pluto, in fact they were understood in great detail. The point is that Jupiter is gravitationally dominant in its orbit. Thousands of other objects are in resonant orbits (the Trojan minor planets), in effect "controlled" by the gravitation of Jupiter. Similarly there are several small asteroids now known which are in resonant orbits with the Earth, this latest being the first that qualifies, though just barely, as a Trojan. By contrast, Pluto and the other plutinos are in orbits which are gravitationally resonant with Neptune, though not 1:1 resonances. It is nearly guaranteed that there are no true "Trojans" for the minor planets/dwarf planets Eris and Pluto, both because their masses are so low and because Neptune’s gravitation runs the show out there. Neither of them is the gravitationally dominant object in the Kuiper Belt. By this dynamical definition, there IS NO major planet in the Kuiper Belt.

  14. Peter Eisenhardt

    The credit for the WISE image of 2010 TK7 at top should be
    NASA/JPL-Caltech/UCLA, not Connors and Wiegert.
    (see http://www.jpl.nasa.gov/spaceimages/details.php?id=pia14405)
    This is a single frame from WISE in its 4.6 micron band
    taken in early October 2010, days after the cryogen was
    exhausted, but while NASA’s planetary division continued
    to fund WISE survey operations to complete coverage
    of the inner edge of the asteroid belt. NEOWISE
    software identified 2010 TK7 as an unknown moving object
    from over a dozen such single frames and reported it to the
    minor planet center (MPC) within a few days of this observation. Connors’ team recognized it as a potential Earth Trojan from
    the MPC listing, and obtained the observations confirming it
    as the first Earth Trojan.

    The object is quite faint in WISE data and I was surprised that he
    NEOWISE software was able to pick it up.

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