Last Saturday, at a workshop organized by the Foundation Questions Institute, Nobel laureate physicist Gerard 't Hooft gave a few informal remarks on the deep nature of reality. Searching for an analogy to the symmetries of basic physics, he asked the attendees to imagine what would happen to our solar system if you suddenly swapped Earth and Mars. He went on to discuss his ideas for explaining quantum mechanics, but I couldn't get my mind off his question. What would happen?
Obviously, Martians would be delighted with the new arrangement. A fairly modest increase in Mars's temperature would melt the polar caps and liberate gases from the soil, flipping the Martian climate into a new, cozier state nearly as warm as Earth. In an article for us in 1999, planetary scientist Chris McKay envisioned terraforming Mars by building factories to pump out greenhouse gases—proving that one man's poison is another's elixir—but moving the planet closer to the sun would certainly do the trick, too. Earthlings would get the short end of the deal. Sunlight would be half as intense and the planet would freeze over. On the plus side, we'd instantly be half as many years old.
In grand scheme of things, though, you might think that nothing would change. According to Kepler's laws, the mass of a planet has almost no effect on its orbit; the mass of the sun is what controls things. Even though Earth is 10 times heavier than Mars, it would still trundle along Mars's old path. Both Mars and Earth are perpetually falling toward the sun, and all falling bodies fall at the same rate.
But Kepler's laws don't account for the subtle gravitational perturbations that planets exert on one another. By rearranging the planets, you perturb these perturbations, and it's not obvious what would happen. So I posed the question to planetary physicist Renu Malhotra of the University of Arizona, who was one of the first scientists to recognize that the planets migrated around early in the history of the solar system. Her initial guess was that Earth's proximity would thin out the asteroid belt, but that the planets' orbits would not be destabilized, at least not right away. She offered to run a computer simulation to check.
The results are a bit surprising. The planetary switch-a-roo makes the inner solar system strongly chaotic. Although none of the inner planets gets flung out of the solar system within the first 10 million years, all undergo large variations in their orbital distances. On occasion, Mars dips inward to become the second rock from the sun. To capture these variations, Malhotra found that she had to use a smaller time increment in the simulations than she had predicted, and consequently each computer run took nearly a day to complete.
To speed things up, she tried ignoring the planet Mercury—standard practice in perturbative calculations, on the assumption that Mercury is so piddling that its gravity is immaterial. Not in this case, though. Without Mercury, the other three inner planets went haywire in a few million years. Mars shot off into deep space. The sensitivity to Mercury's absence is further proof that the altered system would be strongly chaotic.
The graph at left shows the actual solar system. For each planet, Malhotra plots the range of orbital distances: perihelion (closest approach to the sun), aphelion (farthest) and semimajor axis (midpoint). As Pierre-Simon Laplace showed in the late 18th century, our solar system is stable. The semimajor axes are constant, and the shapes of orbits vary modestly on a variety of periods, from tens of thousands to millions of years.
The next graph shows the altered system. Notice how wide the range of orbital distances for each planet has become. For Earth, that's because it's now closer to Jupiter; for Mars, because it's the monkey in the middle. Venus changes hardly at all, while Mercury gets batted around like a pingpong ball. Malhotra's simulation also included the outer planets, but I leave them off, because they lumber on as if nothing had changed.
These results support the emerging view, discussed in our pages by Doug Lin several years ago, that the solar system lives on the edge of chaos. It was probably unstable in its formative years. Planets got reshuffled or ejected until the survivors' orbits were sufficiently well spaced. Any major change would push the system over the edge again. It's analogous to a coffee cup. If you see a cup that is filled exactly to the rim, you can reasonably conclude that some coffee got spilled over the side, and anything you do to the cup would probably spill some more.
Malhotra has supported this viewpoint in the past, but cautions that the solar system is more stable than its age might imply, so the whole question remains unresolved. "Isn't it interesting?" she wrote me. "This kind of thing is what attracted me to planetary dynamics."
Photo courtesy of NASA; graphs courtesy of Renu Malhotra