Geoscience Reference
In-Depth Information
Chapter 5
Gravity
5.1 Introduction
Seismic methods for determining the internal structure of the Earth require the
recording and analysis of energy that has passed through the Earth, energy which
was produced either by earthquakes or artificially by exploration teams. Gravi-
metric and magnetic methods are different in that they utilize measurements of
existing potential fields, which are physical properties of the Earth itself.
5.2 Gravitational potential and acceleration
Two point masses
m
1
and
m
2
at distance
r
apart attract each other with a force
F
,
Gm
1
m
2
r
2
F
=
(5.1)
where
G
is the gravitational or Newtonian constant (Fig. 5.1). In the SI system
of units,
G
has a value of 6.67
10
−
11
m
3
kg
−
1
s
−
2
. This inverse square law of
gravitational attraction was deduced by Sir Isaac Newton in 1666. The legend is
that an apple falling from a tree gave him the revolutionary idea that the force
that attracted the apple downwards could also account for the Moon's orbit of the
Earth.
The acceleration of the mass
m
1
due to the presence of the mass
m
2
is
Gm
2
/
×
r
2
towards
m
2
(since acceleration equals force divided by mass), and the acceleration
of the mass
m
2
is
Gm
2
/
r
2
towards
m
1
.
The
gravitational potential V
due to mass
m
1
can be defined
1
as
Gm
1
r
V
=−
(5.2)
The gravitational potential energy of a mass
m
2
at distance
r
from mass
m
1
is
r
.Ifmass
m
2
moves away from mass
m
1
to a new position,
r
,
the gravitational energy that is released is
Gm
1
m
2
r
−
Gm
1
m
2
/
Gm
1
m
2
r
−
1
The standard convention is to define
V
=
Gm
1
/
r
.
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