Like all spinning celestial bodies that are or once were fluid, the Sun is oblate. Its waist bulges, but ever so slightly. That makes the Sun’s oblateness—the fractional difference between its equatorial and polar radii—difficult to measure, especially with ground-based instruments constrained by atmospheric turbulence. Robert Dicke and coworkers at Princeton University tried hard half a century ago. They hoped to discover a departure from spherical symmetry large enough to affect Mercury’s orbit and reconcile its known precession rate with Dicke’s alternative theory of gravity.

Successive measurements by various groups over the next decades made it clear that the Sun’s oblateness was only about a part in 105, much smaller than what’s required by Dicke’s modification of general relativity. But half a century of solar-oblateness measurements from the ground, from balloons, and recently from space have yielded results suggesting that the Sun’s shape might in fact be variable....

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