Geodesy is the science of measuring and understanding the Earth. It involves determining the size, shape, and gravitational and magnetic fields of the Earth. Geodesy uses measurements from satellites, GPS, and fieldwork to model the Earth as a flattened ellipsoid with parameters like semi-major and semi-minor axes. An accurate mathematical model of the ellipsoid is needed for scientific and practical applications involving the representation of the Earth's shape.

1. ❖ Geodesy is the division of science associated
with the measurement and portrayal of the
Earth.
❖ Geodesy, known also as geodetics, is intimately
concerned with the determination of the size
and shape of the Earth, as well as its elements.
❖ These Earth-based elements include its
terrestrial gravity, magnetic field, tides,
geologic and crustal movement, and polar
motion.
❖ GIS employs these forms of terrestrial
measurement through various data sources,
such as satellite, GPS, and field measurements.
Ocean
Geoid
Earth surface
Gravity Anomaly
Basics of Geodesy
GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

2. ❖ To adequately represent the shape of the Earth in scientific and
real-life applications, a calculable, formula-driven figure of the
Earth is needed.
❖ In its most basic sense, an Earth ellipsoid is a flattened sphere that
bulges in the middle and has two imaginary lines traversing its
core: one from north to south and one from east to west. Each
imaginary line is called an axis.
❖ The ellipsoid’s flattening causes two unequal axes: a longer axis
and a shorter axis
❖ The north-to-south axis through the Earth’s core is the shorter axis
and, as such, is called the minor axis or polar axis.
❖ The east-to-west axis through the Earth’s core is longer and is
called the major axis or equatorial axis
Mathematical Model of the Earth GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

3. ❖ The Earth’s ellipsoid is an ellipse rotated upon its
minor axis, which is functionally called the axis of
rotation or axis of revolution. The purpose of a
mathematical model is to simplify calculations.
❖ Due to the Earth’s symmetry and to minimize
complexity, the mathematical model targets one
quadrant in the ellipse and imparts six key
parameters for calculation.
GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

4. ❖ The six parameters are the
• Semi major axis
• Semi minor axis
• Flattening
• Inverse flattening
• Eccentricity,
• and second eccentricity.
❖ In brief, the flattening of the ellipse is directly related to
the differences in both the semi major and semi minor
axes. It is represented by the formula
Flattening f= (a-b)/a
GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

5. ❖ Earth’s flattening is sometimes displayed as a reciprocal
called the inverse flattening.
❖ For instance, a flattening of 0.003389831 (or 1/295) can
be portrayed as an inverse flattening of 295.
❖ Eccentricity e is the first eccentricity, whereby the
descriptor first is typically implied. It measures the degree
of flattening as the relationship between the focal radius,
or radius from the center point to the foci (i.e., F1, F2),
and the semimajor axis.
GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

6. ❖ Second eccentricity e ′ measures the degree of flattening
as a relationship between the focal radius and the
semiminor axis.
❖ Eccentricity (first and second) is constant throughout the
entire ellipse and ranges from 0 to 1, or more simply from
an ellipsoid with no flattening (circle) to one totally flat
(line). Since a circle has no flattening, its eccentricity
equals zero (e = 0). As e becomes larger and approaches
1, the ellipse becomes flatter until it is a straight line (e =
1).
GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

7. GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

8. GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)

9. ❖ Basically, every GIS and geographic information product is based upon
a reference ellipsoid, which is defined as a standard ellipsoid with
proven and measured parameters.
❖ The reference ellipsoid enables GIS to define point locations with
regional accuracy.
❖ Throughout the years, numerous reference ellipsoids have been
developed by various geodesists with measurements taken at different
source points on Earth.
❖ These reference ellipsoids are only slightly dissimilar. Because of this
differentiation in source data locations, certain reference ellipsoids
work better than others for certain applications and for certain regions.
❖ Unlike Bessel 1841 and other major area-specific ellipsoids, WGS84 is
much more universal and, as a result, is one of the most widely used
reference ellipsoids available.
Reference Ellipsoids
GIS
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)