If it were unburdened by planets, our sun would spin in one spot, like a perfectly balanced top. Instead, like a dog on a short chain, the sun traces small "circles" in space. It is tugged off center as it follows the gravitational pull of enormous Jupiter. If you stood on one of Fischer's fat planets and looked back at our solar system, you would not see Jupiter. But the sun would appear to creep right, then backward, then left, and then forward, in concert with Jupiter's 12-year orbit.

Astronomers would analyze the sunlight for the tiniest shifts in its wavelength, wrought by the sun's backward-forward motion. The degree of wavelength-shift would indicate the speed with which the sun was chasing a planet. That, in turn, would reveal the planet's size. The duration of one backward-forward cycle would equal the duration of that planet's orbit.

So far, the planets caught in the mathematical net are a strange bunch. They are giants, in the size range of Jupiter, which weighs 300 times more than the Earth. And they are probably gaseous, like Jupiter. Their orbits, however, are utterly foreign.

A dozen of these giants orbit 10 times closer to their stars than Earth orbits the sun. And the closer a planet orbits, the faster it travels.

One of these star-huggers, which was recently observed (mathematically) crossing the face of its star, celebrates a new year every three and a half days.

The rest of the giants adopt oddly elliptical orbits. The planets in our own solar system, by contrast, pursue near-circular paths. It may be that ours represents the rare, happy family.

"These planets are probably born on a circular orbit," Fischer says, "and then something perturbs them." The perturber might be a cruel sibling. Two planets, if they pass too closely, could find themselves doing a gravity twirl that would warp both their orbits, possibly hurling one sibling clear into space.