Geoscience Reference
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2.4 Gravimetry
2.4.1 Absolute Gravimetry
Absolute gravimetry (absolute gravity measurement) is a technique utilized to
determine the gravity value (actually, gravitational acceleration) at a defined
geometric point. There are two methods for absolute gravity measurement, one
using a reversible pendulum, and the other by means of the free-fall motion of
bodies. The second method of measurement has been the dominant method since
the 1960s and will be discussed here.
Free-fall motion refers to the accelerated linear motion of a body along the
plumb line under the action of gravity only. According to mechanics, if the gravity
acceleration g in the course of motion along the plumb line is assumed constant
(no gravity changes with height), then the equation of motion is:
1
2
gt
2
,
l
¼
l
0
þ
V
0
t
þ
ð
2
:
25
Þ
where V
0
and l
0
denote the initial velocity of the falling body and the distance from
the origin O, respectively, at the computational time t
0, and l is the distance of
the falling body from the origin O after a period of time t, cf. Fig.
2.18
.
Two methods can be used to determine the gravity value by means of the free-
fall motion of bodies: the free-fall method and the symmetrical rise-and-fall method
(abbreviated as the rise-and-fall method). Their principles are discussed below.
¼
Free-Fall Method
In (2.25), to avoid determining V
0
and l
0
, it is necessary to measure from at least
three positions. Assume at time t
1
, t
2
, and t
3
that the distances of the falling body
from the point O are l
1
, l
2
, and l
3
, respectively, as illustrated in Fig.
2.19
, where the
transverse axis indicates time and the ordinate axis indicates distance. With refer-
ence to (2.25), for each time period there will be a corresponding equation of
motion which gives:
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