Physical forcing of the shelf seas: what drives the motion of ocean? - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 42

GME
d 2

ER o 2

¼ ð 2 : 18 Þ

where R is the radius of the Earth's movement (see Fig. B2.1 ). This balance is exact
only at the centre of the Earth. While the centrifugal force per unit mass Ro 2 is the
same for all points on the Earth, the gravitational pull of the Moon varies in
magnitude and direction over the Earth's surface. It is this small difference between
the gravitational and centrifugal forces which is responsible for generating the tides.
To see how the magnitude and direction of the Tide Generating Force (TGF) can be
calculated, look at Fig. B2.2 , which represents the Earth-Moon system as viewed
from above the plane of the lunar orbit.

Figure B2.2 The Tide
Generating Force (TGF) as the
vector difference of attractive
and centrifugal forces. The upper
diagram is an expanded version
of the vector triangle at P.

z

q

P

GM/d 2

α M

TGF

GM/r 2

P

TGF

a E

r

ω

α M

q

E M

d

C g

Moon

Earth

At an arbitrary point P, the attractive force of the Moon is different from that at the
centre of the Earth; it is directed along the line PMwhich is at an angle a M to the line of
centres and it is also slightly larger because the distance PM is less than EM. The TGF at
P can be calculated by taking the vector difference between the gravitational attraction at
P and the centrifugal force. The resulting vector triangle is shown enlarged in Fig. B2.2 ;
the magnitude of the centrifugal force, which is the same at all points on the Earth, is the
same as the gravitational attraction at the centre of the Earth where the two forces are in
exact balance. Taking the difference of the horizontal components of the forces in the
vector triangle, and allowing for the fact that the radius of the Earth a is small compared
with d, we find that the horizontal component of the TGF can be expressed as:

3
g sin 2

3
2

M
E

a E
d

F H ¼ ð 2 : 19 Þ