DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

tidal formation of solar system
from the source of the gravitational field. The
tidal acceleration is a relative acceleration (locally)
proportional to the gradient of the gravitational
acceleration, equivalent to the second
derivative of the potential, φ,ij , and is also proportional
to the separation ɛ i between the points
considered. Here the subscript “,” denotes partial
derivative.
Hence
(δatidal) j =−ɛ i φ,ij .
A similar expression, involving the Riemannian
tensor, is found in general relativity (so φ,ij is
called the Newtonian (analog of the) Reimannian
tensor).
Because they are proportional to the gradient
of the gravitational acceleration, tidal forces
are proportional to r −3 , and so rise sharply at
small distances but become negligible at large
distances. Typically, tidal forces deform planets
and moons. On the Earth, both the solid body
of the Earth and, more noticeably, the surface
of water in the oceans reacts to these relative
accelerations, in the form of tides, because of
interactions with both the sun and the moon.
In fact, because it is closer, the moon generates
higher tides on the Earth than does the sun.
Far from the ocean shores, the height of the lunar
tidal wave is 65 cm, and the height of the
solar tidal wave is 35 cm. These waves travel
around the Earth because the Earth rotates. The
tides become much higher at the shores because
of local topography (when the tidal wave goes
into a funnel-shaped bay, its width is decreased,
and so the height must increase) or because of
resonances. The latter happens in the Bay of
Fundy in Canada, where tidal waves reach the
height of 16 m.
Because tidal forces deform a solid body (a
planet or moon), tides dissipate energy and act to
decrease rotation. As a result, the rotation is decelerated
until it becomes synchronous with the
orbital motion — which means that afterwards
the planet or moon faces its companion body always
with the same side. This has happened to
our moon in its orbit around the Earth.
tidal formation of solar system A theory
attributing the formation of the solar system to
a close tidal encounter with another star, which
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drew material out of the sun to condense into
planets. This theory is now out of favor because
it suggests solar systems are rare, since such
encounters are rare, while recent observations
provide evidence for planetary systems around
a number of local stars, and even around neutron
stars.
tidal friction As a result of the anelastic response
of the Earth, the peak of its tidal bulge
lags the maximum tidal force by about 12 min.
Because the Earth rotates faster than the moon
orbits the Earth, the tidal bulge leads the Earthmoon
axis by about 3 ◦ . This lag angle causes
a torque acting on the Earth to slow down its
rotation, resulting in a length-of-day increase of
over 2 msec per century. This effect is called
tidal friction. The same torque acting on the
moon increases its orbiting speed and hence the
Earth–moon distance. There is also tidal friction
between the Earth and the sun, about 1/5 of
the strength of the lunar tidal friction.
tidal heating The process by which a body’s
interior heat is generated by the gravitational
tidal forces of external bodies. Tidal deformation
leads to friction, which in turn creates internal
heat. For the Earth’s moon, tidal heating
occurred for only a short period, until its orbit
became circularized and synchronous (when
the rotation period exactly equals the orbital period).
However, if the moon is in a resonance
with another moon, as in the case of several
moons of Jupiter, the rotation can fail to become
locked, and the tidal heating stage can last
much longer. This is the situation with Jupiter’s
moons of Io and Europa. The combination of
Io’s proximity to massive Jupiter and its orbital
resonance with Europa causes tremendous tidal
heating and gives rise to the active volcanism
seen on Io’s surface. Europa is slightly further
from Jupiter than Io, so it feels less of Jupiter’s
tidal forces, but it also is in a resonance (with
Ganymede), and this situation causes some tidal
heating on Europa, which may allow for a liquid
water ocean to exist under its icy crust.
tidal inlet An opening between the sea and
a sheltered estuary or river.