This time-lapse showing the motion of asteroid Phaethon through the sky was captured by amateur astronomer Ingvars Tomsons from Riga, Latvia.



Many astronomers soon began to suspect that Phaethon was a member of a collection of asteroids known as the Pallas family or Palladians. This is a group of small asteroids with highly-inclined orbits and a B-type chemical composition very similar to that of Pallas. Researchers believe they are fragments ejected from Pallas by impact events. (A large impact might have caused Pallas’ huge axial tilt.)Like Pallas and the Palladians, Phaethon has a highly inclined orbit, and is also a B-type asteroid. But could Phaethon migrate from a Palladian family-like orbit in the main belt to a comet-like orbit that nearly grazes the Sun and swings past Earth? And if so, how?Todorović nailed down the Phaethon-Pallas connection by probing the chaotic complexities of orbital resonances. These “are places in our solar system responsible for the transportation of small bodies, something like dynamical highways,” she explained. Astronomers have long known that there are areas in the asteroid belt — called Kirkwood gaps after the astronomer who first noticed them — that are almost completely empty of objects. These regions, said Todorović, have been cleared out by orbital resonances moving small bodies away. “Jupiter, the most massive planet, produces the strongest ones,” Todorović explained. “One is the 5:2 mean-motion resonance with Jupiter, which is approximately 2.8 AU [1 AU is the average Earth-Sun distance] from the Sun,” in the middle of the asteroid belt. “We call it 5:2 because this is a place where asteroids make five orbits around the Sun while Jupiter makes two.”Imagine the situation, said Todorović, where an asteroid and a planet are orbiting the Sun, and the mutual distance between them is smallest at the same point on their respective orbits. When this alignment repeats periodically (and always occurs at the same point), the asteroid and the planet are in an orbital resonance. However, the effects of gravitational interactions between them will begin to accumulate over time, and the smaller body (in this case, the asteroid) will eventually be moved out of its orbit.“Being in a resonance can have dramatic results for an asteroid,” said Todorović. “It can collide with a planet, fall into the Sun, or even be ejected from the solar system. Or the asteroid may spend some time trapped in the resonance” until it’s peacefully moved away to another part of the solar system. Could this be what happened to a member of the Palladian family — a smallish fragment of Pallas was caught in a gravitational whirlpool and flung into a new orbit?

Ingvars Tomsons/Kobalts/Wikipedia

Researchers can use powerful computers and mathematical tools to play “what-if” with simulated Palladians moving through the asteroid belt’s Jovian 5:2 mean-motion resonance (MMR). In 2010, Julia de Leon of the Instituto de Astrofisica de Canarias and her colleagues followed the evolution of simulated orbits for a thousand virtual Pallas fragments that passed through the 5:2 and 8:3 MMRs with Jupiter. Over a period of 100 million years, most ended up in the Sun or ejected into interstellar space. But not all. About 2 percent ended up in Phaethon-like NEA orbits.They also compared the spectra of Phaethon with Pallas, the Palladian family asteroids, and all the other B-type asteroids in the belt. Phaethon turns out to have a visible spectrum very similar to those of the Palladian family objects — and unlike any other B-type asteroid in the main belt.A 2 percent probability is always greater than zero. But it’s still miniscule. Todorović took a closer look. Like de Leon and her colleagues, said Todorović, “we took test objects, placed them into the resonance close to Pallas, and observed where the test objects would go in the following millions of years.”But Todorović used more realistic orbital inclinations and took “snapshots” of chaos inside the resonance region. “I 'took a photo' of the 5:2 resonance, a ‘dynamical map,’ where I could see clearly the exact shape of the resonance. Then I ‘zoomed in’ on the part of the resonance where the fragments of Pallas were injected.” By doing this, she could tease out the fine structure of chaos in the resonance. Todorović then ran computer simulations of how their orbits evolved over 5 million years.“The practical role of these fine lines of chaos is that they provide fast transportation routes. I chose all the test object along the fast transportation roads. The [simulated fragments] were initially placed at the most unstable parts of the resonance were very quickly pushed away by the resonance.”The result? The simulation, which included the effects of chaos in the resonance regions, showed that about 44 percent of the simulated Pallas fragments placed in the 5:2 MMR ended up in Phaethon-like orbits. The first fragments reached Phaethon’s orbit in less than 300,000 years. The median delivery time was 1.7 million years. For fragments that started from the 8:3 MMR, nearly 47 percent arrived in Phaethon’s orbit within 5 million years. The first ones took a little over half a million years.Todorović also used more realistic orbital inclinations for her test fragments. “In a previous study, I used initial particles at low orbital inclination but still in the 5:2 MMR,” she explained. “In that experiment, only 8 percent reached the orbit of Phaethon…. Increasing the inclination of the test objects from 10 to 35 degrees” — the inclination of Pallas — “improved the efficiency of the transportation.”