Asteroid Flyby Yields New Thinking

It was refreshing to see the news media show general restraint when asteroid 2011 MD zipped 7,600 miles from Earth on June 27th. I didn't spot any over-the-top headlines or crazy reporting about potential collisions with Earth. Instead, this rogue rock passed by uneventfully and put on a pretty good show for amateur astronomers equipped with good scopes and blessed with dark skies.

Change in asteroid 2011 MD's orbit
The close pass of 2011 MD changed the asteroid's aphelion distance from about 1.05 to 1.10 astronomical unit (about 5 million miles) and altered its orbital inclination. Click on the diagram for a larger view.
Even though 2011 MD never got brighter than about 11th magnitude, its close flyby did trigger some interesting changes.

First, the asteroid's orbit was yanked around quite a bit. Not only did it pass very close to Earth — well inside Earth's ring of geosynchronous satellites on its outgoing leg — but the asteroid also sped by relatively slowly. This put it within our planet's gravitational grip long enough to bend its trajectory significantly, causing the orbit to expand outward, as shown at right.

Steven Chesley, a member of the Jet Propulsion Laboratory's team of solar-system dynamicists, calculates that 2011 MD's trajectory was bent by 130°. "I don't recall ever seeing such a large turning angle for any other object," notes JPL's Paul Chodas. The close pass also reoriented the orbit's tilt by more than 5°, according to Andrea Milani, a near-Earth asteroid (NEA) specialist at the University of Pisa.

But a second consequence of the close pass has more to do with how Chesley, Chodas, and Milani do their computations — and showed that a little tweaking was in order.

Path of asteroid 2011 MD (side view)
During 2011 MD's close flyby in late June, Earth's gravity bent the little asteroid's trajectory by about 130° (exaggerated in this side-view projection). As a consequence, the inclination, or tilt, of 2011 MD's orbit changed by several degrees.
Soon after the flyby, as the asteroid receded into the depths of space, observers noticed that 2011 MD wasn't exactly following its calculated escape route. In some cases the positional mismatch was as great as 20 arcseconds — shockingly bad, given the all the precise positional data reported by professional and amateur observers worldwide.

It didn't take long to track down the error's cause. "The passage of 2011 MD was such a close approach that the orbit was significantly affected by the shape of the Earth," Milani explains. Our planet isn't a perfect sphere but instead is slightly oblate — squashed pole to pole by about 26½ miles (42½ km) relative to its equator, about one part in 300. This slight out-of-roundness causes, in turn, slight deviations from a perfectly spherical gravitational field, which geophysicists adjust for using a fudge factor known as J2.

Path of asteroid 2011 MD past earth
The path of asteroid 2011 MD near Earth. The dot for each date corresponds to 0h Universal Time.
Once dynamicists recalculated 2011 MD's trajectory with J2 included, the positional errors reported by observers largely disappeared. So why weren't the calculations done this way to begin with? "The answer is that it is an very insignificant term for almost all objects," Chodas explains, "and yet it would add somewhat to the computational load. The object has to make an extremely close approach to the Earth for this term to make a difference, say, within 10 Earth radii," or about 40,000 miles.

"Never before 2011 MD has an asteroid passed at a few Earth radii and been observed both before and after the encounter," Milani points out.

So even though June's interloper never posed a threat to Earth (nor will it in the foreseeable future, according to both JPL and NEODyS), its visit taught the world's asteroid watchers a useful lesson that will pay dividends during future close calls.

Frame from video of 2011 MD's flyby
From his Barred Owl Observatory in Carp, Ontario, Andre Paquette recorded the passage of asteroid 2011 MD with a 14-inch Schmidt-Cassegrain telescope. His took exposures every 2 seconds with a CCD camera, yielding a remarkable video that shows the asteroid's changing brightness as it tumbled by.
Andre Paquette
As a consequence, the NEODyS asteroid-tracking system maintained by Milani and others has been tweaked. "We have implemented a model of Earth's gravity field including oblateness," he reports, "which kicks in only when the distance from the geocenter is less than 0.001 astronomical unit," or about 90,000 miles. The JPL modelers will likewise invoke J2 as needed.

"Our work with NEA orbits and impact monitoring is research work, not routine, even though we have been doing it for more than a decade," comments Milani. "These cases in which we have to upgrade the software, although not frequent, keep happening — and we do not expect they will stop, because we are certainly still in the learning phase."

11 thoughts on “Asteroid Flyby Yields New Thinking

  1. Bob D

    A similar case can be made about the widely-quoted date of July 12 2011 for the date of the completion of Neptune’s first orbit since discovery. This date is out by over 24 hours because it is based on an analysis of heliocentric longitude rather than barycentric longitude, a distinction that is rarely required. Using barycentric coordinates, the correct return date is Monday July 11 (and we can specify a time to within 15 minutes). A full analysis and careful calculation, together with the reasoning behind the choice of the barycenter rather than the Sun, can be found at Regards, Bob D

  2. Anthony BarreiroAnthony Barreiro

    This asteroid was too faint for my little telescope, light-polluted sky, and limited skills. But Andre Paquette’s video shows it quite nicely, moving across the sky for four hours. The light curve is especially interesting, helps me imagine that little rock tumbling through space. I just wish youtube had options for slow motion and frame-by-frame. And it’s good to know that our ability to model the universe is slightly more accurate now.

  3. Larry McNish

    Could the oblate-spheroid dynamics adjustment resolve some or all of the anomalies discovered after the Earth gravity-assist maneuvers of the Galileo, NEAR Shoemaker, and Rosetta spacecraft? (
    Sine dynamists are now fairly certain why the Pioneer spacecraft are slowing down, ( this could strike all these anomalies off the "unknown mysteries" list.

  4. Peter WilsonPeter Wilson

    As long as they don’t start using GR. A correction for oblateness, I can understand. But, "the Ricci curvature tensor…which represents the amount by which the volume element of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in a Euclidean space." Give me a break! And if they have to include dark-energy to make their calculations fit, then their observations are just way too precise.

  5. Bob D

    @Peter: the size of the GR correction due to a swing around a planet can be estimated as half the Schwarzschild radius of the planet multiplied by the angle of deviation in radians. This asteroid was deviated by 130º – if you stick the numbers in, we’re talking about errors of the order 10 millimetres (less than a thousandth of an arc second).

    So you’re right – not too much to worry about there.

    On the other hand, if you have a satellite going round and round, clocking up the radians, and you’re relying on it for accurate positioning, you really will need GR.

    (But not dark energy. That would be silly.)

  6. Allen Robnett

    As long as the orbiting object has a mass that is very much smaller than that of the central object, the mass of the orbiting object has an immeasurable effect on its orbit. Otherwise, an astronaut executing a space walk from the ISS would not stay with the ISS in orbit.

  7. Bob D

    The mass has no importance to its trajectory; but it would have been important if it were on a collision course. Mass has to be estimated using assumptions about its density and its volume, which themselves are estimated from its colour and brightness. NASA NEOP put it at 1900 tonnes – too small for its gravity to noticeably disturb a satellite at a hundred yards, too small to get through our atmosphere without disintegrating, but big enough to put on a fine display if it did.

  8. Frank Reedx

    Obviously dynamicists who work with objects passing near the Earth have been including J2 (and higher order corrections) for decades, and over a century if you count the specialists who analyzed the orbit of the Moon. Saying that this flyby resulted in "new thinking" is very "polite". This was no more than an oversight in the implementation of their software. In other words, they found a bug.

  9. Frank Reedx

    Allen, you wrote: "Otherwise, an astronaut executing a space walk from the ISS would not stay with the ISS in orbit." Actually, though, astronauts would indeed drift away from the ISS if they were not tethered. The local tidal field of the Earth is greater than the gravitational attraction of the space station.

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