166
5. Tides
(Fig. 5.7). The Moon's path around the Earth is elliptical with the closest
distance to the Earth of 357 000 km, perigee, and the farthest distance
of 407 000 km, apogee. The periodicity of the Moon's movement along its
elliptical path is 27.55 days. When the Moon is at perigee, the Moon's tideproducing force is up to 20% higher than its average value, and when the Moon
is at apogee, the tide-producing force is up to 20% smaller than its average
value.
5.2.2 The Earth-Sun System
So far, we have neglected any influence of the Sun on the tide-producing force.
The Sun's mass is about 27 million times larger than that of the Moon, so we
might expect that it would be far more important in producing tides. However,
the Sun is 387 times more distant from the Earth than is the Moon (see Table
5.1). Using these numbers in Eq. (5.21), one finds that the tractive force due
to the Sun is about 46% of the force due to the Moon.
The solar-induced components of the tides are influenced by the Sun's declination. This declination varies over a yearly cycle, and ranges 23.5° either
side of the equatorial plane. Similarly to the Moon's orbit around the Earth,
the orbit of the Earth around the Sun is elliptical. When the Earth is closest
to the Sun, it is said to be in perihelion, and when the Earth is at maximum distance, it is said to be in aphelion. The difference between perihelion
and aphelion is only about 4% of the difference between perigee and apogee
(Bearman, 1997).
Tide-producing forces due to the Sun and the Moon are additive. Thus, the
resulting tide height is a superposition of tide height produced by the Moon and
that produced by the Sun. To illustrate the interaction between these forces
we consider a simpler case when the declinations of the Sun and Moon are both
zero. In Fig. 5.8 four configurations of the Sun and Moon and resulting tides
are shown diagrammatically. A total cycle of events takes 29.5 days. In each
case, we are looking down on the Earth from above the North Pole. In the
cases a and c, the Earth, the Moon and the Sun are all approximately in line,
which corresponds to the New and the Full Moon, respectively.
The tidal bulges of the Moon and Sun are additive, and the resulting tidal
range will be extreme, i.e. the high tide will be higher, and the low tide will be
lower than average. These tides are known as spring tides. The occurrence
of the spring tides is not related to the season, rather the term is derived
from the Anglo-Saxon word springan, which means a rising or welling of the
water (Komar, 1976). During spring tide the Sun and Moon are either in
conjunction (at New Moon - see Fig. 5.8a) or in opposition (at Full Moon
- see Fig. 5.8c). Sometimes it is said that the Moon in both situations is
in syzygy. When the Sun and the Moon act at right angles to each other
(see Fig. 5.8b and 5.8d), it is said that they are in quadrature. Tidal range,
produced by the Sun and the Moon, is correspondingly smaller than average;
these tides are known as neap tides.
5. Tides
(Fig. 5.7). The Moon's path around the Earth is elliptical with the closest
distance to the Earth of 357 000 km, perigee, and the farthest distance
of 407 000 km, apogee. The periodicity of the Moon's movement along its
elliptical path is 27.55 days. When the Moon is at perigee, the Moon's tideproducing force is up to 20% higher than its average value, and when the Moon
is at apogee, the tide-producing force is up to 20% smaller than its average
value.
5.2.2 The Earth-Sun System
So far, we have neglected any influence of the Sun on the tide-producing force.
The Sun's mass is about 27 million times larger than that of the Moon, so we
might expect that it would be far more important in producing tides. However,
the Sun is 387 times more distant from the Earth than is the Moon (see Table
5.1). Using these numbers in Eq. (5.21), one finds that the tractive force due
to the Sun is about 46% of the force due to the Moon.
The solar-induced components of the tides are influenced by the Sun's declination. This declination varies over a yearly cycle, and ranges 23.5° either
side of the equatorial plane. Similarly to the Moon's orbit around the Earth,
the orbit of the Earth around the Sun is elliptical. When the Earth is closest
to the Sun, it is said to be in perihelion, and when the Earth is at maximum distance, it is said to be in aphelion. The difference between perihelion
and aphelion is only about 4% of the difference between perigee and apogee
(Bearman, 1997).
Tide-producing forces due to the Sun and the Moon are additive. Thus, the
resulting tide height is a superposition of tide height produced by the Moon and
that produced by the Sun. To illustrate the interaction between these forces
we consider a simpler case when the declinations of the Sun and Moon are both
zero. In Fig. 5.8 four configurations of the Sun and Moon and resulting tides
are shown diagrammatically. A total cycle of events takes 29.5 days. In each
case, we are looking down on the Earth from above the North Pole. In the
cases a and c, the Earth, the Moon and the Sun are all approximately in line,
which corresponds to the New and the Full Moon, respectively.
The tidal bulges of the Moon and Sun are additive, and the resulting tidal
range will be extreme, i.e. the high tide will be higher, and the low tide will be
lower than average. These tides are known as spring tides. The occurrence
of the spring tides is not related to the season, rather the term is derived
from the Anglo-Saxon word springan, which means a rising or welling of the
water (Komar, 1976). During spring tide the Sun and Moon are either in
conjunction (at New Moon - see Fig. 5.8a) or in opposition (at Full Moon
- see Fig. 5.8c). Sometimes it is said that the Moon in both situations is
in syzygy. When the Sun and the Moon act at right angles to each other
(see Fig. 5.8b and 5.8d), it is said that they are in quadrature. Tidal range,
produced by the Sun and the Moon, is correspondingly smaller than average;
these tides are known as neap tides.