Mid-semester Exam On Environmental Geography

MID-SEMESTER EXAM ON ENVIRONMENTAL GEOGRAPHY 1. Describe the meaning and benefits of geoid in the scope of geodesy and geomatics! 2. Is geoid the same as mean sea level (MSL)? Explain! 3. Explain how to determine geoid undulation geometrically! 4. Describe the meaning of gravitational acceleration, centrifugal acceleration, gravity and gravity anomaly! 5. Is the value of gravity at the North/South Pole greater than its value at the Equator? Give your explanation! ANSWER Number 1 a) Definition Geoid is an equipotential plane of the earth's gravity equipotential plane that coincides with an 'ideal' surface. While in the ocean, the geoid is the ideal sea surface (assuming: no currents, waves, etc.). Geoid undulation is caused by the distribution of mass on Earth. Experts define Geoid as an equipotential plane of the earth's gravity field that coincides with the undisturbed mean sea level, where this plane is continuous through land and sea. b) Benefits Geoid acts as a mathematical and fission model that has an irregular shape. In the field of geodesy, the prospect of determining a high-resolution precise geoid is utilized for: • Transforming geodetic height to orthometric height such as determining orthometric height with GNSS. • Determining the depth of the sea in a bathymetric survey. • Determining height with the LIDAR technique from Synthetic Aperture Radar • Vertical unification Number 2 Mean Sea Level is the sea surface that is free from all variations in sea level that are free from all variations that depend on time (stationary sea level), ideally within a period of 18.61 years. While the geoid is the actual zero surface, used for measuring height or elevation defined by gravity. The difference between the two is undulation (N). However, in practical purposes, geoid and MSL are considered the same in coastal areas. Number 3 Geoid undulation N (large geoid storage against the ellipsoid) obtained from the height difference between the earth's surface against the geoid H (orthometric height) and the earth's surface against the ellipsoid h (geodetic height). In terms of equations, it can be seen as follows 𝑁 =ℎ−𝐻 The above equation can also be used to determine undulations using GNSS. By using astro-geodetc leveling, the determination of the geoid slope between two points dN, where when the geoid undulation at point A (NA), then the undulation at the other point (NB) can be determined. Herlmert's equation can be seen as follows: 𝑑𝑁 = − 𝜀 𝑑𝑠 𝐵 𝑁𝐵 = 𝑁𝐴 − ∫ 𝜀 𝑑𝑠 𝐴 With, 𝜀 = 𝜉 cos 𝛼 + 𝜂 sin With, 𝜀 = Φ−𝜑 𝜂 = Λ − 𝜆 cos𝜑 Number 4 a. Gravitational Acceleration Gravitational acceleration is a circular motion force that rotates away from the center of the circle where the value is positive which is influenced by the force of gravity, expressed using the gravitational acceleration vector 𝑎⃗ in the mass 𝑚𝑝, as a result of the influence of the force 𝐹⃗ from the mass 𝑚𝑄. This is described by Newton's Second Law of motion 𝐹 = 𝑚𝑎, with the following equation: ⃗⃗⃗⃗𝑝⃗ = 𝑎 ⃗𝐹⃗⃗𝑝⃗ 𝑚𝑎 = −𝐺 2 𝑚𝑝 𝑙𝑃𝑄 b. Centrifugal Acceleration Centrifugal acceleration is a function vector of time that is affected by changes in 𝜑 due to polar motion and changes in 𝜔 due to meteorological processes, ocean tides, and the mass transfer of the earth's core. Centrifugal acceleration c is the gradient or first derivative of the centrifugal potential Φ, which can be seen in the following equation: 𝜀 =∇Φ ={ 𝜕Φ 𝜕Φ 𝜕Φ , , } 𝜕𝑥 𝜕𝑦 𝜕𝑧 c. Gravity Gravity is a force acting on a stationary object on the surface of the earth. Gravity is obtained from the resultant of the earth's gravitational force with the centrifugal force due to the rotation of the earth on its axis. Things that affect gravity are the compression of the earth and the rotation of the earth, the heterogeneous and anisotropic nature of the earth's mass, changes in coordinate positions, variations in topography - bathymetry and sea-earth tides. The commonly used units of gravity are 1 gal = 1000 mgal = 1 cm/s-2 d. Gravity Anomaly A gravity anomaly is a visualization of the difference in gravity between one region/area and another. Number 5 The value of gravity at the North/South Pole is greater than the value of gravity at the Equator. This is due to the difference in the long axis of the two regions. Due to the centrifugal force, the shape of the earth is not perfectly round but rather an ellipsoid or obligate. This causes the long axis of the North/South pole region to be shorter than the long axis of the Equator, so that the gravity at the equator will be greater than the North/South pole.