156
5. Tides
5.2 Tide Generating Forces and Equilibrium Theory
5.2.1 The Earth-Moon System
To determine the forces needed for generation of tides we first have to consider
the basic mechanisms involved in the process. Ocean water partly covers the
Earth which moves in space, and in the same time rotates around its own axis.
The rotating Earth is attracted by the Moon and the Sun. The forces which
generate tides result from the balance of these two mechanisms. Initially, for
simplicity, we will neglect the attraction induced by the Sun and consider the
Earth-Moon System first.
Nature of Gravitational Force. Gravitational force, or gravity, is the most
obvious of nature's forces. It keeps us on the ground, and it controls the behaviour of the Universe. Isaac Newton was the first to realize that all bodies
with mass attract each other. In 1687, in his Principia Mathematica, he laid
the conceptual foundation of universal gravitation, discovering that the gravitational force, Fg , between two bodies is proportional to the product of their
mass and inversely proportional to the square of the distance between them.
Applying Newton's law to the Earth and Moon, we obtain (Godin, 1972):
(5.1)
in which mE and mM are the masses of the Earth and Moon, respectively, REM
is the distance from the centre of the Earth to the centre of the Moon, and
G is the universal gravitational constant (G = 6.67 x 1O-1l Nm 2 /kg- 2 ). For
convenience, in Table 5.1 some relevant quantities for the Earth, Moon and
Sun have been listed.
Let us now demonstrate a practical application of Newton's law of universal
gravitation by calculating how the apparent weight of an astronaut's body will
change when he travels from the Earth to the Moon. For simplicity we assume
that the astronaut's weight on Earth is 75 kg (weight) in the metric system.
Using the relationship given in Appendix B, we find that weight in SI unit
will be WE = 75 kg (weight) = 75x 9.806 N ~ 735.45 N. Therefore, the mass
of the body is mb = W E/ 9 = 75 kg. This simple derivation is given here to
stress the difference between weight and mass, and between former and new
unit systems. These differences are discussed in detail in Appendix B.
The gravitational force acting on the astronaut's body on Earth can be calculated from Eq. (5.1):
(5.2)
in which mb is the mass of the astronaut, mE is the Earth's mass, and RE is the
distance between centres of mass of the astronaut and the Earth. We simply
take RE as the mean Earth radius. The astronaut's mass will not change as
5. Tides
5.2 Tide Generating Forces and Equilibrium Theory
5.2.1 The Earth-Moon System
To determine the forces needed for generation of tides we first have to consider
the basic mechanisms involved in the process. Ocean water partly covers the
Earth which moves in space, and in the same time rotates around its own axis.
The rotating Earth is attracted by the Moon and the Sun. The forces which
generate tides result from the balance of these two mechanisms. Initially, for
simplicity, we will neglect the attraction induced by the Sun and consider the
Earth-Moon System first.
Nature of Gravitational Force. Gravitational force, or gravity, is the most
obvious of nature's forces. It keeps us on the ground, and it controls the behaviour of the Universe. Isaac Newton was the first to realize that all bodies
with mass attract each other. In 1687, in his Principia Mathematica, he laid
the conceptual foundation of universal gravitation, discovering that the gravitational force, Fg , between two bodies is proportional to the product of their
mass and inversely proportional to the square of the distance between them.
Applying Newton's law to the Earth and Moon, we obtain (Godin, 1972):
(5.1)
in which mE and mM are the masses of the Earth and Moon, respectively, REM
is the distance from the centre of the Earth to the centre of the Moon, and
G is the universal gravitational constant (G = 6.67 x 1O-1l Nm 2 /kg- 2 ). For
convenience, in Table 5.1 some relevant quantities for the Earth, Moon and
Sun have been listed.
Let us now demonstrate a practical application of Newton's law of universal
gravitation by calculating how the apparent weight of an astronaut's body will
change when he travels from the Earth to the Moon. For simplicity we assume
that the astronaut's weight on Earth is 75 kg (weight) in the metric system.
Using the relationship given in Appendix B, we find that weight in SI unit
will be WE = 75 kg (weight) = 75x 9.806 N ~ 735.45 N. Therefore, the mass
of the body is mb = W E/ 9 = 75 kg. This simple derivation is given here to
stress the difference between weight and mass, and between former and new
unit systems. These differences are discussed in detail in Appendix B.
The gravitational force acting on the astronaut's body on Earth can be calculated from Eq. (5.1):
(5.2)
in which mb is the mass of the astronaut, mE is the Earth's mass, and RE is the
distance between centres of mass of the astronaut and the Earth. We simply
take RE as the mean Earth radius. The astronaut's mass will not change as