Geoscience Reference
In-Depth Information
the object
s potential energy. An object falls along the
eld
lines towards the Earth
'
centres of mass. This is known as the Universal Law of
Gravitation and is the reason that objects are
s centre of mass in order to min-
imise its potential difference with the Earth
'
'
towards the Earth. The attractive force (F) between the
two masses (m
1
and m
2
) separated by a distance (r)is
'
pulled
s mass. Simi-
larly, if a magnetic object is moved across the equipotential
surfaces of a magnetic
field, the object
'
'
s magnetic potential
energy is changed.
G
m
1
m
2
r
2
Þ
The constant of proportionality (G) is known as the
universal
F
¼
ð
3
:
3
3.2.1
Mass and gravity
gravitational
constant.
In the
SI
system
of measurement
it has
an approximate
value of
The essential characteristics of gravity can be explained in
terms of mass, density and the gravity equation. Mass (m)
is the amount of the matter contained in an object. Density
(
10
-
11
m
3
kg
-1
s
-2
.
If we suspend an object in a vacuum chamber (to avoid
complications associated with air resistance), and then
release it so that it falls freely, it will be attracted to the Earth
in accordance with the Universal Law of Gravitation. The
object
6.6726
) is the mass contained in a unit volume of the matter, i.e.
mass per unit volume, and is a measure of the concen-
tration or compactness of a material
ρ
is mass. It is a funda-
mental property of all matter and depends on the masses
and spacing of the atoms comprising the material. Both
quantities are scalars (see
Section 2.2.2
)
. Mass is given by:
'
s velocity changes from zero, when it was suspended,
and increases as it falls, i.e. it accelerates. This is acceleration
due to gravity and it can be obtained from
Eq. (3.3)
as follows.
Consider a small object, with mass m
2
, located on the Earth
'
s
surface. If the mass of the Earth is m
1
and its average radius is
r, entering the relevant values into
Eq. (3.3)
gives:
'
Mass
¼
density
volume
ð
3
:
1
Þ
and from this
mass
volume
F
¼
9
:
81m
2
ð
3
:
4
Þ
Density
¼
ð
3
:
2
Þ
The attractive force acting on the object, due to the mass of
the Earth, is the object
The SI unit of mass is the kilogram (kg) and the unit for
the units kg/m
3
; however, it is common in the geosciences
to use grams per cubic centimetre (g/cm
3
). The two units
differ by a factor of 1000 and, based on 1000 kg being equal
to 1 tonne (t), sometimes densities are specified as t/m
3
, i.e.
2650 kg/m
3
'
is weight, which is proportional to the
object
1kg),the
average acceleration caused by the mass of the Earth, i.e.
gravity, at sea level is approximately equal to 9.81 m/s
2
.
Acceleration due to gravity is the same for all objects of any
mass at the same place on the Earth. However, it does vary
over the Earth owing to the Earth
'
smass.Forabodywithunitmass(m
2
¼
2.65 g/cm
3
. The definition of a
gram is the mass of 1 cm
3
of pure water at 4 °C. This means
that a density is quantified relative to that of an equal volume
of water, i.e. a substance with a density of 2.65 g/cm
3
is 2.65
times as dense as water.
The mass distribution and shape of an object are linked
by the object
2.65 t/m
3
¼
¼
'
s rotation, variations in its
radius and variations in its subsurface density; and also varies
with height above the Earth
'
ssurface(see
Section 3.4
).
Accordingly, a body
'
s weight changes from place to place.
3.2.1.2
Gravity measurement units
Changes in gravitational acceleration associated with dens-
ity changes due to crustal geological features are minute in
comparison with the average strength of the Earth
is centre of mass. It is the mass-weighted
average position of the mass distribution and, therefore,
the point through which gravity acts on the object. For
symmetrical objects of uniform density, like a sphere, cube,
sheet etc., the centre of mass coincides with their geometric
centres (
Fig. 3.2a
).
'
s gravity
field. The SI unit of acceleration is metres/second/second
(m/s
2
) and in the cgs system of measurement the unit is the
gal (1 gal
'
1 cm/s
2
), but they are so large as to be imprac-
tical for gravity surveying. Instead, a speci
c unit of gravity
has been de
ned in the cgs system of measurement and
is known as the milligal (mgal, where 1 mgal
¼
3.2.1.1
The gravity equation
All objects attract one another with a force proportional to
their masses and, for spherical masses whose sizes are
much smaller than the distance between them, inversely
proportionally to the square of the distance between their
10
-
3
gal
¼
10
-
5
m/s
2
). It is still in common use as there is no de
ned SI
unit of gravity. An alternative unit known as the gravity unit
(gu), which is 1
¼
m/s
2
(10
-
6
m/s
2
), is also used (1 mgal is
μ
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