Caption: A diagram illustrating the tidal force and how tidal locking is effected.

Features:

1. Unlike most orbital motion illustrations, the orbital revolution and axial rotation are both chosen to be clockwise.

   In the Earth-Moon system, this means that we are viewing the system from the south celestial pole (SCP) side of the celestial sphere.

2. The situation is a small astro-body orbiting a much larger astro-body.

   The situation is similar to that of the Moon and the Earth.

3. The small astro-body has orbital rotation angular velocity ω and axial rotation angular velocity Ω. The units of the angular velocities could be, e.g., degrees per day.

4. The tidal force causing the small astro-body to become tidally locked is the differential gravitational force on the small astro-body exerted by the large astro-body.

5. The differential gravitational force (i.e., the tidal force) arises because gravitational force between the astro-bodies falls off with distance by inverse-square law (i.e., 1/r**2).

   So the near side of the small astro-body is pulled on more strongly than the far side.

   Both near and far side are in orbit around the large astro-body. The near side does need more gravitational force than the far side since it has smaller orbit.

6. The tidal force---stretches the small astro-body to some degree along the line between the two astro-bodies.

7. The bulges that appear on the body are called tidal bulges and are shown clearly in the upper right image of the small astro-body.

8. This upper right image is what one would see if the small astro-body were already tidally locked to the large astro-body.

   When tidally locked, the small astro-body has Ω = ω, and so always turns the same side facing the large astro-body.

9. The lower right image of the small astro-body is what one sees if the small astro-body is NOT already tidally locked to the large astro-body and has Ω > ω.

10. The axial rotation angular velocity is perpetually rotating the tidal bulges away from alignment with the line between the astro-bodies and the tidal force keeps trying to reform or migrate the tidal bulges back into aligment.

11. The tidal force is now NOT only stretching the small astro-body, but also acting to decelerate its axial rotation angular velocity by acting on the tidal bulges: the gravitational force pulls more strongly one way on the near bulge than it does on the far bulge in the other way.

12. In time, the tidal force will reduce to Ω to ω, and then one has tidal locking (i.e., Ω = ω) and the tidal bulges will be permanently aligned and there is NO more deceleration.

13. If the system started with Ω < ω, then the tidal force would have accelerated the axial rotation angular velocity until tidal locking was achieved again.

14. Actually, there are always perturbations that act to disequalize the two angular velocities of the small astro-body. But the tidal force acts as a restoring force to damp out the effects of the perturbations and drive the small astro-body back toward being exactly tidally locked.

15. The tidal locking is never exact, but always being driven toward being exact.

    From another perspective, the tidal locking is EXACT ON AVERAGE.

16. We would call tidally locked state a stable state since perturbations cannot change it.

17. Actually, virtually all real continually static systems are stable. Perturbations try to move the system, but a restoring force damps them out.

    For example, tall buildings sway with wind perturbations, but keep returning to being nearly exactly upright.

18. The tidal force acts on the large astro-body too trying to drive it to be tidally locked to the small astro-body.

    But the larger astro-bodies in mutually orbiting pairs because of their larger mass almost always initially have more axial rotation angular momentum (resistance to change of axial rotation angular velocity) than smaller astro-bodies. Also the smaller astro-bodies have smaller tidal forces than larger astro-bodies. The result of these two conditions is that it takes longer, often much longer, for the larger astro-bodies to become tidally locked to the smaller astro-bodies, than vice versa.

19. Besides perturbations, there is another complication to tidal locking. Even during one orbit there is NOT exact tidal locking or a fixed degree of tidal locking.

    This is due to libration---which we won't describe here---see Wikipedia: Libration if you must.

20. In the Solar System, most significant moons (including all the major moons) are tidally locked to their parent planets. However, some minor moons are known NOT to be tidally locked because either they have been only recently been captured by their parent planets and tidal locking has NOT yet been established or perturbations may be so strong that tidal locking CANNOT be established.

    Actually, the axial rotation angular velocity of many minor moons are NOT perfectly known, and so it is NOT known if they are tidally locked or NOT.

    For some information concerning Solar System moons that are NOT tidally locked, see Wikipedia: Tidal locking: Occurrence: Moons.

21. What about tidal locking of planets in the Solar System?

    Among the planets, only ex-planet Pluto is tidally locked (see Wikipedia: Tidal locking: List of known tidally locked bodies). Pluto and its largest moon Charon are mutually tidally locked.

    If you were on the Charon/Pluto-facing side of Pluto/Charon, you would always see Charon/Pluto in the sky at the same location relative to the ground and with its Pluto/Charon-facing side turned toward you.

    The other planets have NOT become tidally locked to their moon of strongest tidal force for the reasons given above. Also the effect of the multiple tidal forces (due multiple moons and the Sun) acts against tidal locking to the moon of strongest tidal force.

    Why are NO planets tidally locked to the Sun?

    Although the Sun has the strongest gravity, its tidal force is too weak as it turns out even for Mercury where it is strongest. Actually, Mercury is an unusual case because it has a 3:2 spin-orbit resonance (see Wikipedia: Mercury: 3:2 spin-orbit resonance). We will NOT go into this complex case.

22. What is the status of the tidal force of the Moon's on the Earth?

    The Moon's tidal force on the Earth is slowing down the Earth's rotation, and thus increasing the length of the day.

    However, the slowing rate is so slow that the Earth will probably NOT become tidally locked to the Moon before the Sun's red giant phase in ∼ 5 Gyr (see Wikipedia: Sun: After core hydrogen exhaustion) when the Sun may well vaporize Earth and Moon (see Wikipedia: Tidal acceleration: Effects of the Moon's gravity)---lucky us.

23. The tidal force has another important effect besides trying to causing tidal locking.

    If the orbit of an astro-body about another astro-body is NOT circular (i.e., has non-zero eccentricity), the tidal force varies with the orbital radius: stronger when orbital radius is smaller, weaker when orbital radius is larger.

    The varying tidal force perpetually flexes the astro-body in the noncircular orbit which results in resistive forces inside the astro-body to turn macroscopic mechanical energy from the two astro-bodies's motions into heat energy.

    The heat energy can cause some degree of geologically activity.

24. In the Solar System, Jupiter's moon Io has the strongest tidal force heating of any astro-body. As a result, Io exhibits continual volcanism. Io is the most geologically active astro-body. Earth is a distant second.