ODA BULTUM UNIVERSITY

INSTITUTE OF TECHNOLOGY
DEPARTMENT OF SURVEYING ENGINEERING
Group Assignment of Geodesy II
For 4 th
year, Semester I

Table of Content

1 Introduction ....................................................................................................
1.1 gravity........................................................................................................
1.2 Normal Gravity........................................................................................

INTRODUCTION
Gravity is a fundamental force that attracts two bodies toward each other. In geodesy, gravity is
crucial for understanding the Earth's shape, structure, and dynamics. It is not a uniform force; it
varies across the Earth's surface due to factors such as latitude, elevation, and subsurface
density variations.
Normal gravity refers to the idealized value of gravitational acceleration that one would expect
at a given location according to a theoretical model, typically based on a reference ellipsoid. .
Normal gravity is widely used in geodesy for applications involving the computation of vertical
deflections, geoid modeling, and in the conversion between orthometric and ellipsoidal heights.
The concept of a normal gravity ellipsoid relates to the mathematical representation of the
Earth's shape, typically modeled as an ellipsoid of revolution.
Gravity potential is a scalar quantity representing the potential energy per unit mass at a given
point due to the gravitational field. In geodesy, it provides insight into how gravitational forces
vary across different locations. By analyzing the gravity potential, geodesists can better
understand the geoid and calculate height differences between points in various gravitational
fields, allowing for precise elevation modeling.
Gravitational potential is a broader concept that encompasses the potential energy associated
with the gravitational force within a field. In the context of geodesy, it is used to describe the
gravitational effects of both the Earth and its surrounding bodies. This potential is integral in
determining the Earth's gravitational field and is essential for satellite navigation and precise
geophysical measurements.A gravity anomaly is the difference between the observed gravity
value at a specific location and the expected value based on a standard model, such as normal
gravity. Anomalies can indicate variations in subsurface density, geological structures, or the
presence of resources like minerals or oil.Gravity disturbance refers to local deviations from the
expected gravitational field that arise due to variations in the distribution of mass within the
Earth. These disturbances can be caused by geological features such as mountains, valleys, and
subsurface anomalies.Geopotential is a term that integrates gravitational potential with the
effects of centrifugal forces due to the Earth's rotation. It is a key concept in geodesy as it helps
define the geoid, which is an equipotential surface representing mean sea level across the
globe.Geoid undulation represents the deviation of the geoid from the reference ellipsoid. It
quantifies the vertical distance between these two surfaces at any given point on the
Earth.Normal potential is a theoretical model of gravitational potential that corresponds to a
reference state of the Earth's gravitational field, typically based on an idealized or standardized
mass distribution
1.2 Gravity
Gravity is a fundamental force that attracts two bodies towards each other, with its strength
depending on the masses of the bodies and the distance between them. In geodesy, gravity is
essential for understanding the Earth's shape, rotation, and changes in elevation. The
acceleration due to gravity on the surface of the Earth varies depending on several factors,
including latitude, altitude, and geological structures. Geodesists measure gravity using
gravimeters to obtain precise readings for surveying, geophysical studies, and modeling the
Earth's gravitational field. The measure of gravity is critical for defining the geoid, which is a
reference surface for understanding sea level and land elevation. Gravity also plays a significant
role in geodynamics, helping to describe tectonic movements and the behavior of Earth's
interior.
1.2 Normal Gravity
Normal gravity refers to the theoretical value of gravitational acceleration at a specific location
on Earth, calculated under the assumption of a perfectly smooth and homogeneous Earth. It
provides a standard reference against which variations in gravitational acceleration can be
measured. The concept of normal gravity is essential for geodesy, particularly in the creation of
geodetic models. It is often expressed as gn with a commonly used value of 9.80665 m/s² at sea
level. Normal gravity allows geodesists to differentiate between the regular effects of the Earth's
shape and gravitational field, and the local variations caused by geological structures,
topography, and other factors. Normal gravity forms the basis for understanding how actual
gravitational measurement can deviate from theoretical predictions.
 1.3 Normal Gravity Ellipsoid
The normal gravity ellipsoid is a mathematical model that represents the Earth as a smooth,
geodetic ellipsoid with a uniform gravitational field. This ellipsoid simplifies the complexities of
the Earth's actual shape and gravitational variations. The normal gravity model employs a
reference ellipsoid, such as the WGS84 or the International Terrestrial Reference System (ITRS),
to standardize measurements of gravity. By defining this ellipsoidal shape, geodesists can create
a framework for determining heights and understanding geoid undulations. The normal gravity
ellipsoid provides a basis for the calculation of normal gravity values at various points on the
Earth’s surface, incorporating factors like latitude and altitude to predict how gravity would
behave in an idealized world.

Gravity Potential
Gravity potential is a scalar function that describes the potential energy per unit mass at a point
in a gravitational field. In geodesy, it is denoted as VVV and indicates how much potential
energy a mass would have relative to a reference level, typically taken at infinity or at sea level.
The gravitational potential is particularly important when analyzing the shape of the geoid and
understanding variations in Earth's gravity. It helps geodesists model the Earth's gravitational
field, taking into account the variations in density and structure of the Earth. The potential is a
smooth function, allowing for the calculation of gravitational effects in a variety of applications,
such as satellite orbits and Earth observation.

Gravitational Potential
Gravitational potential refers specifically to the work done against gravity to bring a mass from
infinity to a point in the gravitational field. It is a measure typically expressed in joules per
kilogram (J/kg) and reflects how gravitational forces influence the position of objects. In
geodesy, gravitational potential is crucial for determining the shape of the geoid and
understanding the Earth's gravitational field characteristics. The gravitational potential varies
spatially because of the Earth's uneven density distribution, leading to different gravitational
behaviors in various regions. This variation is paramount for accurate geodetic measurements
and applications involving satellite navigation, where understanding gravitational influences is
critical.
Gravity Anomaly
Gravity anomaly refers to the difference between the observed gravitational acceleration and
the normal gravity value that would be expected at a specific location based on the normal
gravity model. It is an essential factor in geodesy and geophysics, as gravity anomalies can
indicate subsurface geological features, such as voids, mineral deposits, or tectonic features.
Positive anomalies indicate areas where gravity is greater than expected (often due to denser
materials), while negative anomalies indicate areas of lower gravity. Understanding these
anomalies can provide insights into Earth's internal structure and processes, making them
critical for resource exploration and geological hazard assessment.

Gravity Disturbance
Gravity disturbance is a term that describes the local deviation of the gravitational field from the
expected value, accounting for normal gravity and various geophysical phenomena. It takes into
consideration the actual measurements of gravity as affected by local geological conditions such
as mountain ranges, valleys, and subsurface materials. Gravity disturbance is usually measured
using gravimeters and analyzed to further understand the variations in the Earth's gravity field.
This information is crucial for applications in mineral exploration, oil and gas assessments, and
earthquake research, where knowledge of gravitational perturbations can provide insight into
underlying geological structures.
Geopotential
Geopotential is a measure of the potential energy per unit mass in a gravitational field and is
important for geodesic calculations. It expands on the concept of gravitational potential by
accounting for the centrifugal force due to the Earth's rotation and is typically expressed in
geopotential meters (gpm or m²/s²). Geopotential measurements serve as a basis for defining
the geoid and for understanding how the Earth's topography interacts with gravitational forces.
The geopotential surface is the surface of constant potential energy, which is critical in
hydrostatic balance concepts related to atmospheric and oceanic circulation.
Geoid Undulation
Geoid undulation is the height difference between the geoid and a reference ellipsoid at a
specific geographical location. It reflects the variations in Earth's gravitational field caused by
mass redistribution, such as mountains, ocean trenches, and variations in Earth's crust density.
The undulation is measured in meters and illustrates how the actual sea level deviates from a
simple geometrical model of the Earth. Geoid undulation helps geodesists understand the
Earth's physical and gravitational characteristics, informing applications like satellite altimetry
and precise level measurements. The geoid serves as a reference for determining orthometric
heights.
Normal Potential
Normal potential refers to the theoretical potential energy of a unit mass at a point in the
gravitational field created by an idealized sphere or ellipsoid, ignoring local irregularities caused
by the Earth's structure. It serves as a baseline for measuring gravitational potential at the
Earth's surface and is used in geodetic calculations. Normal potential allows for the comparison
of observed gravitational potentials with empirical models, facilitating the identification of
anomalies due to topographical and geological features. Understanding normal potential helps
define the standard reference for height systems and increases the accuracy of satellite
positioning and navigation electronics
Ellipsoidal Height (h):
Definition: The vertical distance from a point above the Earth's surface to the nearest point on
the reference ellipsoid.
Reference Surface: Ellipsoid (e.g., WGS84).
Measurement Method: Typically derived from Global Navigation Satellite System (GNSS)
measurements.
Interpretation: This height is sensitive to the irregularities and variations in the Earth's surface
shape, as it is purely a geometric measure above the ellipsoid.
Orthometric Height (H):
Definition: The vertical distance between a point and the geoid, which represents mean sea
level across the Earth.
Reference Surface: Geoid, which is an equipotential surface that accounts for variations in
gravitational field.
Measurement Method: Usually determined through leveling methods or by correcting
ellipsoidal heights with geoid height data.
Interpretation: This height provides a more practical measure of elevation because it reflects
the actual physical position relative to mean sea level.
Summary of Differences:
h (Ellipsoidal Height) is measured from the ellipsoid, while H (Orthometric Height) is measured
from the geoid.
Ellipsoidal heights are often used in GNSS applications; orthometric heights are more relevant
for engineering, surveying, and applications where altitude above sea level is significant.
Relation Between the Two:
The relation between these two heights can generally be expressed as:
H=h−N
where N is the height of the geoid above the ellipsoid (geoid undulation). This relationship
shows that orthometric height can be derived from ellipsoidal height by subtracting the geoid's
height above the ellipsoid.

References
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applications, Cambridge Univ. Press, Cam bridge
Bronshtein, I. N., Semendyayev, K. A., & Musiol, G., 2004.
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Freeden, W., 1985. Computation of spherical harmonics and
approximation by spherical harmonicex pansions, Report /
Department of Geodetic Science and Surveying, the Ohio State
University; 362,Ohio.
Hackney, R. & Featherstone, W., 2003. Geodetic versus
geophysical perspectives of the ’gravity anomaly’,Geophys.
Jour. Intern., 154(1), 35–43.
Heiskanen, W. A. & Moritz, H., 1967. Physical geodesy, A series
of books in geology, Freeman, SanFrancisco [etal.].
Hobson, E. W., 1931. The Theory of Spherical and Ellipsoidal
Harmonics, Cambridge University Press,Cambridge.
Hofmann-Wellenhof, B. & Moritz, H., 2005. Physical geodesy,
Wien [et al.]: Springer, 2005

THE END!