In Shakespeare's "Julius Caesar," the title character declares, "But I am constant as the Northern Star, of whose true fixed and resting quality there is no fellow in the firmament." In modern astronomical terms, Caesar was saying that he was a flaky, unstable guy. Astronomers have known for some time that Polaris, the North Star, sitting almost directly over the North Pole, is a Cepheid variable, a type of star that is caught in a cycle of bloating and collapsing because it has exhausted its hydrogen fuel. In this unsettled state, Polaris brightens and dims every four days or so,...