Gravimetry is the measurement of gravity.

1. NIRMAL LAMA POLYTECHNIC INSTITUTE
Prepared by:- Er. Dipendra Kr. Yadav
GEODESY AND ASTRONOMY
3. GRAVIMETRY

2. GRAVITY
• Newton, in 1987 discovered the existence of a force between
two masses.
• The force between masses is called gravitational force.
• The gravitational force is always attractive.
• That is each body (or mass) attracts towards it the other body
(or the other mass).
• The force exists among all bodies in the universe.

3. GRAVITY
• In gravitational force, we talk about the force of
attraction between two bodies
• If one body is the earth; the gravitational force is called force of
gravity.
• Therefore the force of gravity is the special case of the force of
gravitation.
• The earth attracts every body lying on its surface or near its
surface towards its center.

4. GRAVITY
• The force of attraction of the earth on the bodies which lie on its
surface (or near its surface) is called gravity or force of gravity
• When a body is released from a height, it falls towards the
earth and, its velocity goes on increasing
• The acceleration on the falling body is produced by the gravity
of the earth.
• Hence the acceleration produced in a body in its free fall from
small height towards the earth is called acceleration due to
gravity.

5. GRAVITY
• The acceleration due to gravity is uniform. It acts in the
direction of line joining the body to the center of the earth.
• It is denoted by g.
• The force of gravity on the body due to the earth is given by
F =
𝐺𝑀𝑚
𝑟2
– where M is the mass of the earth,
– m is the small body of mass falling freely a small height
– G is universal gravity instant G = 6.672 × 10−11 m3s−2kg−1 (or Nm2 kg−2).
– r be the distance of the body from the center of the earth

6. GRAVITY
• The acceleration produced by the earth on the body (i.e. due to
gravity) is given by:
• g =
𝑓𝑜𝑟𝑐𝑒
𝑚𝑎𝑠𝑠
=
𝐹
𝑚
=
𝐺𝑀
𝑟2 i.e. g =
𝐺𝑀
𝑟2
• The unit of censure of g is the gal(1 cm per 𝑠𝑒𝑐2
) or more usually
the milligals.

7. GRAVIMETRY
• Gravimetry is the measurement of gravity.
• Historically, only the measurement of the length of the gravity
vector is meant.
• More recent techniques allow vector gravimetry,
• i.e. they give the direction of the gravity vector as well.
• In a wider sense, indirect measurements of gravity, such as
the recovery of gravity information from satellite orbit
perturbations, are sometimes referred to as gravimetry too.

8. GRAVIMETER
• A Gravimeter is a scientific instrument for measuring the value of gravity
‘g’ at a place
• Absolute gravimeter:-
- the instrument that measures ‘g’ directly is called absolute gravimeter.
- it is large, unwidely and expensive.
• Relative gravimeter:-
- The instrument that can measure only differences in ‘g’ between one
place to another is called relative gravimeter.
- They are cheaper, smaller and more robust.
- For field surveys, it is more usual to use a relative gravity meter.

9. TERMS USED IN GRAVIMETRY
• Absolute gravity:- Absolute gravity is the total acceleration due
to gravity at a point.
• Relative gravity:- Relative gravity is the difference in
gravitational acceleration between two points
• Theoretical gravity:- Theoretical Gravity (v) is the value of
gravity using the following closed formula.
v = 𝑣𝑒
(1+𝑘𝑠𝑖𝑛2)
(1−𝑒2𝑠𝑖𝑛2)2

10. TERMS USED IN GRAVIMETRY
• Where,
k =
(𝑏𝑣𝑝−𝑎𝑣𝑒)
𝑎𝑣𝑒
– a = spheroidal semi major axis in meters. .
– b = spheroidal semi minor axis in meters.
– e= Normal gravity at the equator
– p = Normal gravity at the pole
–  = Latitude

11. TERMS USED IN GRAVIMETRY
• Gravity anomaly:- the
gravity anomaly is the difference
between magnitudes of gravity
‘g’ at P on the geoid and normal
gravity ‘’ at Q on the reference
ellipsoid.
• Referring to the figure, the
gravity anomaly vector is defined
as:

12. GRAVITY ANOMALY
• Gravity anomaly is the difference between the value of
gravity as observed at a station after applying
corrections so as to reduce it to sea level or geoid and
the theoretical value of gravity at sea level as obtained
by Clairut’s formula for international ellipsoid.
• The Clairut's formula for determining the value of gravity
at a place can be either in terms of latitude of a place or
in terms of longitude of a place

13. GRAVITY ANOMALY
• Clairut’s formula in terms of Latitude of the place:
• In terms of the latitude  of the place where the gravity is to be
determined, the Clairut’s formula is given by:
• gt = ge{1+Sin2 + C Sin22} gals
Where,
• gt = theoretical value of gravity at latitude 
• ge= gravity value at equator (978.049 gals)
•  = constant (0.0052884) C
= constant (-0.0000059)
• Then the formula may be written as:
• gt = 978.049{1+0.0052884Sin2 - 0.0000059 Sin22} gals

14. GRAVITY ANOMALY
• Clairut’s formula in terms of Longitude of the place:
• In terms of the Longitude L of the place where the gravity is to be determined, the Clairut’s
formula is given by:
• gt = 𝑔𝑒{1+Sin2 + C Sin22 +  Cos2Cos2(L-L0)} gals
• Where,
• L = longitude of the place of observation.
L0 = reference longitude (=0)
• gt = theoretical value of gravity at latitude 
• ge= gravity value at equator (978.049 gals)
•  = constant (0.00529)
• C = constant (-0.000007)
•  = constant (0.000419)
• Therefore, gt = 978.049{1+0.00529Sin2 - 0.000007 Sin22+0.000419 Cos2Cos2(L-L0)}gals.

15. USES OF GRAVITY ANOMALY
• Gravity anomaly helps to determine the shape and size of
the earth by computing the following data required
– Computing the flattening value of the meridian.
– Shape of the geoid in comparison to the reference ellipsoid.
– It also helps in computing the deflection of the vertical for
reduction of the base lines from geoid to spheroid.
– Over mountainous, it helps to correct the error of closure in
triangulation .
– It helps to study the nature of the crust of earth.

16. USES OF GRAVITY ANOMALY
– The determination of the deflection of the vertical helps to reduce the
base line from geoid to the reference ellipsoid, which is truly a
mathematical ellipsoid, so that all computations over the world can be
compared.
– The separation of geoid from reference ellipsoid can be determined by
using the value of gravity anomaly in stoke s formula.
– It helps to unify the geodetic nets over the earth regardless of their
separation to by oceans
– It also helps how the earth tends toward equilibrium.
– In the field of geophysics, it gives geological data for interpretation by
seismology and geomagnetism

17. APPLICATIONS OF GRAVIMETRY
• Gravity survey has application in the solution of a
number of problems including:
– First order triangulation Network
– Leveling.
– The determination of the shape of the Earth
– Deviations of the vertical.
– Geoids/ Spheroid Separation.
– Mineral Exploration.
– Certain navigational problems.
– The evaluation of satellite orbits