Text 4

1. Read and translate the text:

Introduction of Triangulation

The idea of triangulation was apparently conceived by the Danish astronomer Tycho Brache before the end of the 16^th century, but it was developed as a science by a contemporary Dutch mathematician Willebroad van Roijen Snell. He used a chain of 33 triangles to determine the length of an arc essentially in the way customarily done today. The resulting size of the Earth, however, was 3.4 percent too small.

In 1669 Jean Picard, a French astronomer, first used a telescope in determining latitude and in measuring angles in triangulation that consisted of 13 triangles and extended from Paris to 1.2˚ northward. His observations and results were extremely important because his length of arc was used by the English physicist and mathematician Sir Isaac Newton in his theoretical calculations to prove that the attraction of the Earth is the principal force governing the motion of the moon in its orbit.

2. Find information about other geodetic methods such as traversing, leveling and radiation. Discuss in groups the key features of these methods.

Text 5 The Main Geodetic Concepts

1. Make word combinations and translate them:

1. celestial

2. opposite

3. gravity

4. direction

5. angular

6. spin

7. topocentric

8. local

9. meridian

10. local

11. south

12. observational

1. pole

2. plane

3. meridian

4. coordinates

5. angle

6. sphere

7. height

8. axis

9. point

10. vector

11. concept

12. observer

2. Read and translate the text:

Here we define some basic observational concepts, like angles and coordinates, defined in geodesy (and astronomy as well), mostly from the viewpoint of the local observer.

• The plumb-line or vertical is the direction of local gravity, or the line that results by following it.

• The zenith is the point on the celestial sphere where the direction of the gravity vector in a point, extended upwards, intersects it.

• The nadir is the opposite point, where the direction of gravity extended downward intersects the (invisible) celestial sphere.

• The celestial horizon is a plane perpendicular to a point's gravity vector.

• Azimuth is the direction angle within the plane of the horizon, typically counted clockwise from the north or south.

• Elevation is the angular height of an object above the horizon.

• Local topocentric coordinates are azimuth (direction angle within the plane of the horizon) and elevation angle (or zenith angle) and distance.

• The north celestial pole is the extension of the Earth's (precessing and nutating) instantaneous spin axis extended northward to intersect the celestial sphere (similarly for the south celestial pole).

• The celestial equator is the intersection of the (instantaneous) Earth equatorial plane with the celestial sphere.

• A meridian plane is any plane perpendicular to the celestial equator and containing the celestial poles.

• The local meridian is the plane containing the direction to the zenith and the direction to the celestial pole.

3. Answer the questions:

1. What are the main geodetic concepts?

2. Give definitions to the main geodetic concepts.