Introduction in Geodesy SUMMARY OF GEODESY 1-B Geodesy Astronomical Coordinate Systems. The difference between the plane survey and geodetic survey types of Geodesy. GEOID Spherical excess. Circumpolar. the difference between the plane triangle and the spherical triangle. Plane survey. Geodetic survey.

2. Introduction
Geodesy in its modern terms can be defined as that branch of applied mathematics
which combines the basic mathematics and physical principles to
determine the size & shape of the earth,
SUMMARY OF GEODESY 1-B
Shape of the earth (1)

3. Thedifferencebetweentheplanesurveyand
geodeticsurvey.
 Plane survey
Deals with the earth as plane
surface .
The triangle on the surface is
called plane triangle .
Used in area less than 50 KM .
Less accuracy .
Simple instruments are used
 Geodetic survey
Deals with the earth as a spherical
surface .
The triangle on the surface is called
spherical triangle .
Used in area more than 50 KM .
High accuracy .
Complex instruments are used .

4. types of Geodesy.
geometric, physical and dynamic.
# geometric Geodesy.
“GEOID”. Such a surface is everywhere perpendicular to the gravity
vector; it is a surface of constant gravity potential “W”, equipotential surface.
Thegeoid is much smoother than the topographic surface.
# Geometric geodesy deals mainly with geometrical relationships between
points on the earth’s surface, which automatically leads to the study of the size,
and shape of the earth.

5. Definition (ξ): It's the difference between the plane triangle and
the spherical triangle.
☞ ξ= (A+B+C)-180°
Where: A, B&C are the angles of the spherical triangle.
☞ ξ "=(F/R2 )ρ
Where: R is the radius of the earth
F is the area of the triangle
Ρ is = 1/sin1"

6. the difference between the plane triangle and
the spherical triangle.

7. Spherical Triangles
A spherical triangle is the figure made by connecting 3 points on the surface of a sphere
(not all on a great circle) with arcs of great circles. Great circles are the intersection of the
plane containing the center of the sphere with the surface of the sphere itself. Examples
of great circles on the earth are the equator and meridians of longitude.
The parts of a spherical triangle are called sides and angles. Sides are measured by their
angles subtended at the center of the sphere. In the figures below the sides are labeled
a, b, and c. A, B, and C are the angles opposite sides a, b, and c respectively.
A useful special case is Right Angled Spherical Triangles, where one of the angles is 90
degrees. The equations simplify for this case
General Spherical Triangles
The Law of Sines
sin a/sin A = sin b/sin B = sin c/sin C
The Law of Cosines
cos a = cos b cos c + sin b sin c cos A
cos A = -cos B cos C + sin B sin C cos a

8. The sine of any middle part equals the product of the tangents of the adjacent parts.
The sine of any middle part equals the product of the cosines of the opposite parts. Example:
co-A = 90-A, co-B = 90-B
sin a = tan b tab (co-B) or sin a = tan b cot B
sin (co-A) = cos a cos (co-B) or cos A = cos a sin B
Similar relations hold for the other sides and angles.

9. Napier's Rules for a Right Angled Spherical Triangle
Excluding the right angle C arrange the remaining five parts of the spherical right triangle as shown
in the circle. Label the three parts opposite right angle C with the prefix co- meaning compliment
(90-angle).
Any one part of the circle is called a middle part, the two neighboring parts are called adjacent
parts, and the two remaining parts are called opposite parts.
Napier's Rules are:

11. Types of horizon
Geodetic
horizon
Astronomical
horizon