Moons and planets aren’t point particles, and their finite sizes and lack of rigidity affect their orbits. For example, the Moon’s gravity raises a tidal bulge in Earth’s oceans. Because Earth rotates faster than the Moon orbits, that bulge is always pushed slightly ahead of the line between Earth and the Moon, and the gravitational attraction between the Moon and the bulge pulls Earth backward in its rotation and the Moon forward in its orbit: Our days are getting longer, and the Moon is gaining energy and thus receding.

The same phenomenon occurs between Jupiter and its moons, particularly its innermost large moon, Io. On the other hand, Jupiter also raises a tidal bulge in Io, which causes lo to lose energy. Now the Paris Observatory’s Valéry Lainey and colleagues have teased out the previously unknown magnitudes of the Jovian system’s tidal interactions by analyzing 116 years’ worth of observations...

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