Jupiter and Io the Planet and Its Moon Distort Each Other, with Consequences for Io’S Volcanic Activity and the Orbits of Jupiter’S Other Moons

Analysis quantifies effects of tides & in Jupiter and Io The planet and its moon distort each other, with consequences for Io’s volcanic activity and the orbits of Jupiter’s other moons. Moons and planets aren’t point par- Tides in Jupiter and its inner- ticles, and their finite sizes and lack of a most large moon, Io, have rigidity affect their orbits. For example, opposite effects on Io’s orbit. the Moon’s gravity raises a tidal bulge (a) Io’s gravity creates a tidal in Earth’s oceans. Because Earth rotates bulge in Jupiter, which is pushed faster than the Moon orbits, that bulge by Jupiter’s rotation (red arrows) is always pushed slightly ahead of the ahead of the Io–Jupiter line. line between Earth and the Moon, and Gravitational interaction (black the gravitational attraction between the arrows) between Io and the Moon and the bulge pulls Earth back- bulge slows Jupiter’s rotation ward in its rotation and the Moon for- and increases Io’s orbital energy. ward in its orbit: Our days are getting (b) Jupiter also creates a tidal longer, and the Moon is gaining energy bulge in Io. Because Io has an b and thus receding. elliptical orbit, its instantaneous The same phenomenon occurs be- orbital speed varies (green tween Jupiter and its moons, particu- arrows). At its most distant point from Jupiter, Io rotates (red larly its innermost large moon, Io. On arrows) faster than it orbits, so the other hand, Jupiter also raises a the bulge lies slightly ahead of tidal bulge in Io, which causes Io to lose the Io–Jupiter line in the direc- energy. Now the Paris Observatory’s tion of Io’s rotation. At its nearest Valéry Lainey and colleagues have point to Jupiter, the opposite is teased out the previously unknown true. As a result, Jupiter exerts a magnitudes of the Jovian system’s tidal force on Io that diminishes Io’s interactions by analyzing 116 years’ orbital energy. The tidal bulges worth of observations of the moons’ and orbit eccentricity are exag- orbits.1 gerated for effect. Many moons circular. For example, Io’s and Europa’s bulge that Jupiter generates in the rocky Several dozen of the bodies orbiting point of closest approach, where Europa moon would have little effect, because Jupiter are classified as moons, but the pulls Io outward, is always at the same it would always be aligned with the Io– largest by far are the four discovered by place in their respective orbits. That re- Jupiter line. But the slight ellipticity of Galileo in 1610. In order from nearest to peated tug gives Io’s orbit a nonzero ec- Io’s orbit has two consequences, as farthest from Jupiter, they are Io, Eu- centricity. Furthermore, the Laplace res- shown in panel b. First, as the Io–Jupiter ropa, Ganymede, and Callisto. Europa, onance means that any change in Io’s distance changes, so too does the grav- the smallest of the four, is more than orbit strongly affects both Europa and itational force felt by Io, and therefore 7000 times as massive as Jupiter’s fifth Ganymede, and vice versa. the size of the bulge. Second, because Io and next largest moon, Himalia. Io, Eu- is not always moving at the same angu- ropa, and Ganymede are in a Laplace Battle of the bulges lar speed, its instantaneous orbital and resonance, meaning that their orbital Io is the only one of the Galilean moons rotational rates are not perfectly periods form small-integer ratios: Ap- to have significant tidal interaction with matched. At its farthest point from proximately every seven Earth days, Jupiter. The moon creates a tidal bulge Jupiter—the apojove—Io is spinning Jupiter is orbited by Ganymede once, in the planet (as shown in panel a of the faster than it is orbiting, so the tidal Europa twice, and Io four times. The figure), which increases Io’s orbital en- bulge lies slightly ahead of the Io– resonance has an effect on their orbits ergy at the expense of Jupiter’s rota- Jupiter line in the direction of Io’s rota- and how they influence one another. tional energy. By the virial theorem, tion. Thus Jupiter exerts a torque on Io In isolation from other satellites, when an orbiting body’s energy in- that slows the moon’s rotation and adds moons tend to settle into synchronous creases, its kinetic energy decreases to its orbital energy. At the other side of rotation (meaning that the orbital period while its potential energy increases by the orbit—the perijove—the opposite is equal to the rotational period) and cir- twice as much. So although Jupiter’s occurs: Io is orbiting faster than it is cular orbits. The Galilean moons are in tidal bulge pulls Io forward in its orbit, spinning, the bulge lags behind the Io– synchronous rotation, but because of the its net effect is to slow Io’s motion. Jupiter line, and the planet’s gravity in- Laplace resonance, their orbits are not If Io’s orbit were circular, the tidal creases the moon’s rotational energy at © 2009 American Institute of Physics, S-0031-9228-0908-320-3 August 2009 Physics Today 11 the expense of its orbital energy. And method of secular accelerations doesn’t with most estimates being between since the bulge is larger and the gravi- allow any conclusions to be drawn 2 and 2.5 W/m2. It appears, therefore, tational attraction is stronger at the per- about the tidal magnitudes: Since tides that Io is close to a thermal steady ijove, its influence wins out: Io’s tidal in Jupiter and tides in Io have similar state—that its volcanic activity is driven bulge causes Io to spiral inward toward but opposite consequences for the by the heat generated by tidal friction Jupiter. Much of the energy that goes moons’ orbits, the two effects can’t be now, rather than by heat retained from into growing, shrinking, and shifting decorrelated by looking at the orbital a past period when tides might have the bulge is dissipated through friction; accelerations alone. been even higher. the resulting heat is thought to be re- Lainey and colleagues were the first sponsible for Io’s volcanic activity, the to include the tidal effects directly in a Longer-term trends? most dramatic in the solar system. model. They numerically integrated the Lainey and colleagues reconstructed Which tidal effect is stronger, and orbits, in two-hour time steps, from what happened to Io, Europa, and whether Io’s total energy is actually in- 1891 to 2007. Then they iterated the in- Ganymede over a period of 116 years. creasing or decreasing, depends on how tegration to fit the 26 parameters of But on the time scale of orbital evolu- severely Io and Jupiter are distorted by their model: the initial position and ve- tion, 116 years is just the blink of an eye. tidal forces. Those things can’t easily be locity vectors of each of the four moons What’s next for the Jovian moons? It’s observed from Earth. To infer the tide- (they included Callisto even though it’s hard to tell, because the evolution the induced accelerations from observa- not in the Laplace resonance and researchers found is not sustainable. tions of the moons’ orbits, one must doesn’t interact strongly with the oth- Since Io’s orbital period is shortening track the Jovian moons for a long time. ers) and Jupiter’s and Io’s susceptibility while Europa’s and Ganymede’s are The earliest usable measurements of the to tides. They were able to separate the lengthening, the moons are evolving moons’ positions are photographic two tidal mechanisms because Io’s tides out of their Laplace resonance. Once the plates that date back to 1891. But the po- had a substantial effect on the eccentric- resonance is broken, Io’s orbit will lose sitions must be determined with much ity of Io’s orbit, whereas Jupiter’s tides its eccentricity, so the tidal bulge in Io greater precision than any individual had a much smaller effect. will no longer grow and shrink and will hundred-year-old measurement—or The calculation revealed that Io is no longer be susceptible to torque from even many modern measurements— speeding up and thus spiraling inward Jupiter. That means no more spiraling can provide. Averaging many measure- and losing energy, whereas Europa and inward and, most likely, no more vol- ments helps, but the positions must also Ganymede are slowing down, spiraling canism. The present results don’t offer be constrained through use of a model. outward, and gaining energy: At the any predictions, though, about how end of the 116-year period, Io is 55 km Tides over time soon the resonance will be effectively farther ahead in its orbit than it would broken, how much Io’s orbital energy Several groups in the past have at- have been without any acceleration, Eu- will ultimately decrease, or what will tempted to derive the orbital accelera- ropa is 125 km behind, and Ganymede happen once it starts increasing again. tions of Jupiter’s Galilean moons from is 365 km behind. From Io’s tidal param- “Moving out of resonance and Io’s 2 the records of their positions. But eter, Lainey’s collaborators Özgür inward spiraling are both expressions they’ve always done it by treating the Karatekin and Tim Van Hoolst, geo- of an evolution that cannot persist,” tidal effects as secular accelerations— physicists at the Royal Observatory of says David Stevenson of Caltech.

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