its types and formation
All celestial bodies exert a
gravitational force on each other. These forces of attraction between earth and
other celestial bodies (mainly moon and sun) cause periodical variations in the
level of a water surface, commonly known as tides. There are several theories
about the tides but none adequately explains all the phenomenon of tides.
However, the commonly used theory is after Newton, and is known as the
equilibrium theory. According to this theory, a force of attraction exists
between two celestial bodies, acting in the straight line joining the centre of
masses of the two bodies, and the magnitude of this force is proportional to
the product of the masses of the bodies and is inversely proportional to the
square of the distance between them. We shall apply this theory to the tides
produced on earth due to the force of attraction between earth and moon.
However, the following assumptions are made in the equilibrium theory :
is covered all round by an ocean of uniform depth.
The ocean is capable of assuming instantaneously
the equilibrium , required by the tide producing forces. This is possible if we
neglect (i) inertia of water, (ii) viscosity of water, and (iii) force of
attraction between parts of itself.
1. The Lunar
shows the earth and the moon,
with their centres of masses O1 and O2 respectively. Since moon
is very near to the earth, it is the major tide producing force. To start with,
we will ignore the daily rotation of the earth on its axis. Both earth and moon
attract each other, and the force of attraction would act along O1O2.
Let O be the common centre of gravity of earth and moon. The earth and
moon revolve monthly about O, and due to this revolution their separate
positions are maintained. The distribution of force is not uniform, but it is
more for the points facing the moon and less for remote points. Due to the
revolution of earth about the common centre of gravity O, centrifugal
force of uniform intensity is exerted on all the particles of the earth. The
direction of this centrifugal force is parallel to O1O2 and acts
outward. Thus, the total force of attraction due to moon is counter-balanced by
the total centrifugal force, and the earth maintains its position relative to
the moon. However, since the fore of attraction is not uniform, the resultant
force will very all along. The resultant forces are the tide producing forces. Assuming that water has no inertia and
viscosity, the ocean enveloping the
earth's surface will adjust itself to the
unbalanced resultant forces, giving rise to the equilibrium. Thus, there are two lunar tides at A
and B, and two low wate positions at C and D. The tide at A is called the
superior lunar tide or tide of moon's upper
transit, While tide at B is called inferior or antilunar tide.
Now let us consider the earth's
rotation on its axis. Assuming the moon to remain stationary, the major axis of
lunar tidal equilibrium figure would maintain a constant position. Due to
rotation of earth about its axis from west to east, once in 24 hours, point A
would occupy successive position C, B and D at intervals of 6 h. Thus, point A
would experience regular variation in the level of water. It will experience
high water (tide) at intervals of 12 h and low water midway between. This
interval of 6 h variation is true only if moon is assumed stationary. However,
in a lunation of 29.53 days the moon makes one revolution relative to sun from
the new moon to new moon. This revolution is in the same direction as the
diurnal rotation of earth, and hence there are 29.53 transits of moon across a
meridian in 29.53 mean solar days. This is on the assumption that the moon does
this revolution in a plane passing through the equator. Thus, the interval
between successive transits of moon or any meridian will be 24 h, 50.5 m. Thus,
the average interval between successive high waters would be about 12 h 25 m.
The interval of 24 h 50.5 m between two successive transits of moon over a
meridian is called the tidal day.
2. The Solar
The phenomenon of production of tides due to force of
attraction between earth and sun is
similar to the lunar tides. Thus, there will be superior solar
tide and an inferior or anti-solar tide. However, sun is at a large distance
from the earth and hence the tide producing force due to sun is much less.
tide = 0.458 Lunar tide.
Combined effect : Spring and neap tides
tide = 0.458 Lunar tide.
Above equation shows that the solar tide force is
less than half the lunar tide force. However, their combined effect is
important, specially at the new moon when both the sun and moon have the same
celestial longitude, they cross a meridian at the same instant.
that both the sun and moon lie in the same horizontal plane passing through the
equator, the effects of both the
tides are added, giving rise to maximum or spring tide of new moon. The term 'spring' does not
refer to the season, but to the springing or waxing of the
moon. After the new moon, the
moon falls behind the sun and crosses each meridian 50 minutes later each day.
In after 7 ½ days, the difference between longitude of the moon and that of sun
becomes 90 o , and the moon is in quadrature. The crest of moon tide coincides
with the trough of the solar tide, giving rise to the neap tide of the first
quarter. During the neap tide, the high water level is below the average while
the low water level is above the
average. After about 15 days of
the start of lunation, when full moon occurs, the difference between moon's
longitude and of sun's longitude is 180 o , and the moon is in
However, the crests of both the tides coincide,
giving rise to spring tide of full moon. In about 22 days after the start of
lunation, the difference in longitudes of the moon and the sun becomes 270 o and
neap tide of third quarter is formed. Finally, when the moon reaches to its new
moon position, after about 29 ½ days of the previous new moon, both of them
have the same celestial longitude and the spring tide of new moon is again
formed making the beginning of another cycle of spring and neap tides.
4. Other Effects
The length of the tidal day, assumed to be 24
hours and 50.5 minutes is not constant because of (i) varying relative
positions of the sun and moon, (ii) relative attraction of the sun and moon,
(iii) ellipticity of the orbit of the moon (assumed circular earlier) and
earth, (v) declination (or deviation from the plane of equator) of the sun and
the moon, (v) effects of the
land masses and (vi) deviation of the shape of the earth from
the spheroid. Due to these, the high water at a place may not occur exactly at
the moon's upper or
lower transit. The effect of
varying relative positions of the sun and moon gives rise to
what are known as priming of tide and lagging of tide.
new moon position, the crest of the composite tide is under the moon and
normal tide is formed. For the positions of the moon between
new moon and first quarter, the high water at any place occurs before the moon's transit,
the interval between successive high
Water is less than the average of 12 hours 25 minutes and the
tide is said to prime. For positions of moon between the first quarter and the
full moon, the high water at any place occurs after the moon transits, the
interval between successive high water is more than the average, and tide is
said to lag. Similarly, between full moon and 3rd quarter position, the tide
primes while between the 3rd quarter and full moon position, the tide lags. At
first quarter, full moon and third quarter position of moon, normal tide occurs.
Due to the several assumptions made in the equilibrium theory,
and due to several other factors affecting the magnitude and period of tides,
close agreement between the results of the theory, and the actual field
observations is not available. Due to obstruction of land masses, tide may be
heaped up at some places. Due to inertia and viscosity of sea water, equilibrium figure is not achieved
instantaneously. Hence prediction of the tides at a place must be based largely