Where asteroids and comets are concerned, the solar system is like a giant roller coaster in space. Figuring out how the orbits of these rocks twist and turn around just the sun and one other planet is so hard that brute-force computation is usually the only solution. But in the 1 July print issue of PRL, a team reports an analytical method for describing an asteroid’s likelihood of escaping orbit around a planet. The result, inspired by work on transitions between chemical species during reactions, may eventually give researchers a new tool for analyzing the orbits of the flotsam of the solar system, the authors suggest.
Consider the comet Oterma. Every now and then, it switches from a complicated trajectory outside the orbit of Jupiter to one lying within. Jerry Marsden of the California Institute of Technology and colleagues found they could describe this transition between orbits mathematically in terms of a boundary between initial and final states. To make the transition, the comet passed through a bottleneck near two of Jupiter’s libration points–where objects maintain a fixed distance relative to the planet and the Sun.
When Charles Jaffé, a chemical physicist at West Virginia University in Morgantown, saw the paper reporting the comet theory, he was astonished. “It looks like he stole some of our figures,” Jaffé recalls thinking. He had recently published results using a similar approach for ionized atoms, where he had extended the conventional theory of the transition state a molecule adopts during its switch from reactant to product in a chemical reaction. Realizing they had taken the same approach to solve different problems, the two teams of authors joined forces to apply it to more complicated astrophysical scenarios.
Now they have reported their first step in this direction, using a highly idealized picture of asteroids distributed evenly around Mars and getting stuck in an orbit 200 Martian radii out. Their statistical theory predicts the rate at which rocks eject from this orbit over time. After 40 revolutions, the theory matched numerical simulations to within 1%. “I just found that amazing,” Marsden says. “From a dynamical systems point of view it’s a relatively simple theory.”
The researchers think this mechanism could apply to all sorts of objects orbiting in space, from comets to asteroids to space probes. Marsden points out that spacecraft such as the ongoing Genesis mission–which collects particles from the solar wind–make use of the same kinds of libration points implicated in the Oterma bottleneck. So a simpler description of their trajectories might be beneficial to NASA planners. The team would also like to better understand the process that brings rocks from Mars to Earth.
Martin Duncan of Queen’s University, in Kingston, Canada, is skeptical that the theory in its current state could handle highly complicated regions full of debris, such as the asteroid belt or the Kuiper belt outside Neptune. But if it can predict the escape rate from these areas, “that would be very important for predicting the flux of near-Earth asteroids and Jupiter-family comets,” he says.
The team agrees that the technique isn’t yet ready for such real-world problems but believes it will be in the future. Compared with simulations, Marsden says, theory is starting to produce “much deeper insight into the movement of comets and asteroids and all sorts of stuff that’s floating around through the solar system.”