Why don't planets collide more often? How do planetary systems -- like our solar system or multi-planet systems around other stars -- organize themselves? Of all of the possible ways planets could orbit, how many configurations will remain stable over the billions of years of a star's life cycle?

Rejecting the large range of unstable possibilities -- all the configurations that would lead to collisions -- would leave behind a sharper view of planetary systems around other stars, but it's not as easy as it sounds.

"Separating the stable from the unstable configurations turns out to be a fascinating and brutally hard problem," said Daniel Tamayo, a NASA Hubble Fellowship Program Sagan Fellow in astrophysical sciences at Princeton. To make sure a planetary system is stable, astronomers need to calculate the motions of multiple interacting planets over billions of years and check each possible configuration for stability -- a computationally prohibitive undertaking.

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