# Focus: Earth’s Peculiar Neighbors

Published September 24, 1999  |  Phys. Rev. Focus 4, 16 (1999)  |  DOI: 10.1103/PhysRevFocus.4.16

#### Coorbital Dynamics at Large Eccentricity and Inclination

F. Namouni, A. A. Christou, and C. D. Murray

Published September 27, 1999

An asteroid heading toward Earth makes a good movie plot, but astronomers haven’t yet found any heavenly bodies on such a collision course. There are plenty of asteroids in our neighborhood of the solar system, however, and a team of physicists has now discovered several new types of near-Earth-asteroid orbital motion. In the 27 September PRL they describe their theory and computer simulations of the orbits of three known asteroids. They conclude that although we are safe from collisions with such objects, there may be many asteroids inhabiting these newly discovered orbits, including undiscovered satellites of Earth.

The orbits are examples of “coorbital motion,” where the asteroid is locked into a gravitational dance with a planet and the Sun, rather than orbiting the Sun independently. In one simple type of coorbital motion an asteroid could stay close to Earth’s orbital track, always remaining some distance ahead of Earth as the two bodies orbit the Sun. The asteroid could move slightly faster than Earth, advancing farther around the sun (from Earth’s perspective) with each year. After many years it could advance all the way around the Sun to a point not far behind Earth, before slowing down again and appearing from Earth to turn back the other way.

Asteroid (3753) Cruithne appeared to be in such a “horseshoe” orbit when it was discovered a few years ago, but its highly eccentric (egg-shaped) trajectory and steep inclination with the plane of the solar system couldn’t be explained by current theories, says Fathi Namouni of Queen Mary and Westfield College in London. Namouni and his colleagues developed a theory for coorbital motion based on the long-term average position of the asteroid as the shape and orientation of its elliptical orbit evolves with time. They found several new classes of motion, and unlike previous theories, their predictions are valid for highly eccentric and inclined orbits. To check their predictions, the team ran computer simulations for a few real asteroids to see their orbital tracks ${10}^{5}$ years into the past and future. These asteroids exhibited all of the newly discovered behaviors.

In “retrograde satellite motion”–one of the new classes of motion–an asteroid can slowly orbit a planet at a great distance, perhaps half the distance between the planet and the sun. Cruithne appears to be in a “compound” orbit–a combination of retrograde satellite motion and a modified horseshoe. The team also discovered that high eccentricity asteroids can be temporarily captured by a planet and remain in stable coorbital motion for thousands of years before wandering away: Another asteroid they investigated orbited Earth for 35,000 years before leaving, according to their computations.

Namouni explains that all of the inner planets are protected from collisions with asteroids locked in coorbital motion because the orbits are stable, rather than chaotic. He expects that more asteroids will soon be discovered inhabiting some of these orbital modes, perhaps even orbiting the Earth in a region where no one has yet looked.

The theory “may prove to be important in understanding how planets were formed,” says Scott Tremaine of Princeton University, and it may also allow space mission planners to come up with new gravitational tricks for their space probes. But he says the main significance of the work is that it provides a complete classification of coorbital motions, which should allow a good understanding of other asteroids, including their likelihood of hitting Earth.