By Pasquale Tricarico

Tiny 2004 ST26 made the sixth closest known flyby of the year just before midnight UT last Tuesday, coming just inside the Earth-Moon system. And shortly after midnight it buzzed the Moon at a distance of about 29,400 km. (18,255 miles), or 7.6% of the distance between Earth and Moon. Pasquale Tricarico responded to the question, “Can you separate out how much the change in this object's orbit was due to the influence of the Moon vs. the Earth?” with the following explanation.

I compared two evolutions in ORSA, one with Earth and Moon, the other with a single EM-barycenter body. The evolution of the orbital elements of 2004 ST26 is almost the same, there is not a big difference between the two cases. Of course, there is a small extra kick from the Moon in proximity of the close approach, a small “bump,” as you can see in these graphs showing how the object's eccentricity and semimajor axis changed.

In general it is always true that, if there is some distribution of mass between two objects such as the Earth and Moon, and a third object is far enough away, all it will feel is the attraction of “something” located in the barycenter of the mass distribution. That something has a mass that is the sum of the masses. As the third object gets closer to the mass distribution, it starts feeling something different, due to the non-homogeneous distribution of mass. This is exactly what happened in this case. When 2004 ST26 was far from the Earth-Moon system, the attraction was essentially due to the Earth-Moon barycenter “body.” When it got closer, it felt separate attractions from the Moon and Earth contributions to the mass, and you see the bump, or “kick,” in the smooth curve from the Moon's influence. The smooth progression in the graphs represents the region where the Earth-Moon system can be well approximated by the barycenter, while in the kick region the system is resolved by the asteroid as separate bodies.

Terminology:  The semimajor axis (a) of a heliocentric (Sun-centered) orbit is an object's average distance from the Sun. This value is given in astronomical units (AU), where one AU is the average distance from Earth to Sun, thus the semimajor axis for Earth's orbit is a=1.0. Eccentricity (e) is a ratio measuring how non-circular an orbit is. Except for some comets, this value falls between e=0.0 (perfectly circular) and e=1.0 (not circular but parabolic).