Adapted from Michael Nauenberg / UC Santa Cruz

On track.
A planetary figure-8 orbit is possible, at least temporarily, even if theorists account for the effects of general relativity.

Trick Three-Planet Orbit Remains True

Staff Writer

If a supreme being were so inclined, it could configure three planets so that they would race around one another in a graceful figure-8 orbit. At least that's what Newton's theory of gravity predicts. Now, a team of physicists has shown that the figure-8 orbit is possible even if they use Einstein's more-accurate theory of gravity, general relativity.

When two planets cling to each other through gravity, one will orbit the other by tracing an ellipse over and over. But throw together three or more orbs, and their interactions become so complex that chaos reigns. (Our solar system remains orderly because the sun is so heavy that each planet follows its lead and more or less ignores the other planets.) However, in 1993 physicist Cristopher Moore of the University of New Mexico in Albuquerque discovered that if he set things up just right, then according to Newton's theory, three equal-mass planets could chase each other endlessly in a figure 8.

It wasn't clear that Einstein's theory would allow the figure 8, however. General relativity says that gravity is actually the warping of space and time themselves, and it makes small but profound changes to the predictions of Newton's theory. For example, general relativity predicts that when one planet orbits another body, its orbit will slowly turn, like the hour hand on a clock, producing a complicated flowerlike pattern that doesn't repeat. In fact, once Einstein had completed the theory, he immediately showed that it could account for the theretofore unexplained turning of the orbit of Mercury. The figure-8 orbit ought to suffer from similar distortions.

But Tatsunori Imai, Takamasa Chiba, and Hideki Asada at Hirosaki University in Japan have found that they can fiddle with the precise starting positions and velocities to compensate for the distortions and keep the planets on the figure-8 orbit, at least in the short term. Using a computer to simulate the exact orbit, they find that the planets stay on track for at least 10 cycles, as they report in an upcoming issue of Physical Review Letters. The analysis is the first to show that such an oddball orbit is possible in Einstein's universe.

"This is indeed an interesting and amazing result," says Luc Blanchet, a theoretical physicist at the Institute of Astrophysics in Paris. He notes, however, that in its full glory, Einstein's theory says the circulating planets should also produce ripples in space and time that will gradually carry away the planets' energy. That will eventually spoil the repeating orbit, Blanchet predicts: "I don't expect the figure 8 to remain [indefinitely]."

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