We have introduced
in our earlier discussion of the Moon's
observational characteristics through the effect of the Moon on the
oceans, but the effect is much more general, and has a number of important
Tidal Coupling and Gravitational Locking
Some important consequences of tidal forces in the Solar System include:
Tidal forces will distort any body experiencing differential gravitational
forces. This will normally occur for bodies of finite extent in gravitational
fields because of the strong distance dependence of the gravitational force.
Thus, not only the oceans, but the body of the Earth is distorted by the Lunar
gravity. However, because the Earth is rigid compared with the oceans, the
"tides" in the body of the Earth are much smaller than in the oceans.
There is a limiting radius for the orbit of one body around another, inside
of which the tidal forces are so large that no large solid objects can exist that are
held together only by gravitational forces.
This radius is called the Roche Limit. Thus, solid objects put into
orbit inside the Roche limit will be torn apart by tidal forces, and
conversely, solid objects cannot grow by accreting into larger objects if they
orbit inside the Roche limit. A famous example is the rings of Saturn:
because they lie inside the Roche limit for Saturn, they cannot be solid
objects held together by gravitation and must be composed of many small particles.
Obviously solid objects can exist inside the Roche limit (for example, spacecraft)
but they must be held together by forces other than gravity. This is true of a spacecraft,
where chemical forces between the atoms and molecules are much larger than the gravitational
The tidal forces are reciprocal. Not only will the Moon induce tides in the
body of the Earth and the Earth's oceans, but by the same argument the
gravitational field of the Earth will induce differential forces and therefore
tides in the body of the Moon. Again, because the body of the Moon is quite
rigid these Lunar tides will be very small, but they occur.
This reciprocal induction of tides in the body of the Earth and the Moon leads
to a complicated coupling of the rotational and orbital motions of the two
objects. These tidal forces and associated couplings have the following
The interior of the Earth and Moon are heated by the
tides in their bodies, just as a paper clip is heated by constant bending.
This effect is very small for the Earth and Moon, but we shall see that
it can be dramatic for
other objects that experience much larger differential
gravitational forces and therefore much larger tidal forces.
For example, we shall see that the tidal forces exerted by
on its moon
Io are so large that the solid surface of Io is raised and lowered by
hundreds of meters twice in each rotational period.
This motion so heats the interior of Io that it is
probably mostly molten; as a consequence, Io is covered with active volcanos
and is the geologically most active object in the Solar System.
The tidal coupling of the orbital and rotational motion tends to synchronize
them. In the simplest instance, the period of rotation for the two bodies and
the orbital period eventually become exactly
equal because of this tidal coupling (and as a result, the size of the orbit is
changed in such a way as to conserve
for the entire system).
This is called
gravitational (or tidal) locking, because
as the two objects revolve around their common center of mass each keeps
the same side turned toward the other.
Tidal Coupling in the Earth-Moon System
Thus, the fact that the rotational period of the Moon and the orbital period of
the Earth-Moon system are of the same length is not an accident. Presumably
this was not always true, but over billions
of years the tidal coupling of the Earth and the Moon has led to this
synchronization. In the case of the Earth-Moon system the synchronization is
not yet complete. The Earth is slowly decreasing its rotational period and
eventually the Earth and Moon will have exactly the same rotational period, and
these will also exactly equal the orbital period. At the same time, the
separation between the Earth and Moon will slowly increase in just such a way
as to conserve angular momentum for the entire system.
Thus, billions of years from now the Earth
will always keep the same face turned toward the Moon, just as the Moon already
keeps the same face turned toward the Earth. We will encounter other examples
of such tidal locking in other pairs of objects in the Solar System.