Jupiter's moon Io is tidally locked to Jupiter yet is the most volcanically active body in the solar system. How can tidal heating continue in a tidally locked moon?
AIo is not actually tidally locked; it hasn't had enough time for locking to occur given Jupiter's distance
BTidal locking causes maximum friction in the interior, which is why locked moons are the most heated
CIo's orbital eccentricity — maintained by gravitational resonance with Europa and Ganymede — means its tidal bulge changes size and orientation throughout each orbit, continuously flexing the interior even in the locked state
DJupiter's tidal forces are so extreme that the locked state itself is energetically unstable
Tidal locking synchronizes rotation with orbit, which would eliminate heating if the orbit were perfectly circular — a locked moon on a circular orbit always presents the same face and experiences a constant, unchanging bulge. But Io's orbital eccentricity (maintained by resonance with Europa and Ganymede) means the distance to Jupiter varies throughout each orbit. Even in a locked state, this changing distance causes the tidal bulge to flex in size and direction, dissipating energy as internal friction. The key is eccentricity, not the rotational state: tidal heating requires ongoing deformation, which requires a changing tidal force, which requires an eccentric orbit.
Question 2 Multiple Choice
Two moons of identical size and composition orbit identical planets at the same average orbital distance. Moon A has a circular orbit; Moon B has a highly elliptical orbit. Which experiences more tidal heating?
AMoon A — a constant tidal force produces steady, maximum energy dissipation
BThey experience equal tidal heating because their average orbital distances are the same
CMoon B — orbital eccentricity causes the tidal bulge to flex continuously, generating heat through internal friction
DMoon A — circular orbits are the end state of tidal evolution and therefore represent peak tidal energy
Tidal heating requires ongoing deformation of the moon's interior, which requires the tidal force to change in magnitude and direction. On a circular orbit, the distance to the planet is constant, the tidal bulge is constant in size and orientation, and there is no ongoing flexing — no friction, no heating. On an elliptical orbit, the moon's distance varies continuously, causing the bulge to grow and shrink and shift direction with each orbit, dissipating energy as internal heat. Moon B, with its elliptical orbit, is continuously being squeezed and stretched, while Moon A is in a static configuration. Europa's subsurface ocean is maintained by exactly this mechanism.
Question 3 True / False
Tidal forces on a moon arise from the difference in gravitational pull across the two sides of the moon, not from the average gravitational force the planet exerts on it.
TTrue
FFalse
Answer: True
This differential character is the defining property of a tidal force. If the planet's gravity were uniform across the moon — every part experiencing the same pull — the moon would simply accelerate as a whole with no internal stresses and no tidal bulge. The tidal force is the deviation from uniform acceleration: the near side is pulled harder than the center, and the far side is pulled less than the center. This stretches the moon along the planet-moon axis and compresses it perpendicular to that axis. The tidal force scales as 1/r³ (falling off faster than gravity's 1/r²), so proximity to the planet matters enormously.
Question 4 True / False
Tidal locking means tidal forces on the locked moon have ceased largely, since synchronizing rotation with the orbit eliminates the displaced tidal bulge.
TTrue
FFalse
Answer: False
Tidal locking stops the tidal torque on the moon's spin — the torque that was decelerating or accelerating rotation until the rotation period matched the orbital period. But tidal forces themselves continue acting on the locked moon, stretching it along the planet-moon axis. What locking eliminates is the constant re-orientation of the bulge (which was the source of frictional heating on a circular orbit). If the orbit is eccentric, the varying distance means the bulge changes in size even in the locked state, and tidal heating continues. Tidal forces are a consequence of differential gravity across an extended body and persist as long as the moon has finite size and orbits the planet.
Question 5 Short Answer
Explain why the Moon's gradual recession from Earth (about 3.8 cm per year) is directly connected to the lengthening of Earth's day. What is being transferred between Earth and the Moon?
Think about your answer, then reveal below.
Model answer: Angular momentum is being transferred from Earth's rotation to the Moon's orbit. Earth's rotation creates tidal bulges in its oceans; because Earth rotates faster than the Moon orbits, these bulges are swept slightly ahead of the Earth-Moon line. The Moon's gravity pulls back on these bulges, exerting a torque that slows Earth's rotation (lengthening the day), while Earth's displaced bulges gravitationally pull the Moon forward, adding energy and angular momentum to the Moon's orbit. In orbital mechanics, more energy in an orbit means a larger, more distant orbit — so the Moon recedes. Angular momentum is conserved in the total Earth-Moon system: what Earth's spin loses, the Moon's orbit gains.
This is a beautiful example of angular momentum conservation across a coupled system. The connection between Earth's slowing rotation and the Moon's recession is not coincidental — they are the same physical process viewed from two perspectives. Running it backward, the Moon was much closer to Earth early in solar system history and Earth rotated much faster (a day was perhaps 6 hours long 4 billion years ago). Laser ranging experiments precisely measure the Moon's recession at 3.82 cm/year, providing direct confirmation of the tidal angular momentum transfer mechanism.