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Question 1

Ellipsoid vs Geoid Earth Models

Answer 1

• Ellipsoid is the idealized shape of the earth that includes distortion due to rotational forces.
• Geoid is the idealized shape of the earths ‘Sea Level’ that includes distortion due to rotational forces and the gravitational effects of land masses.

Question 2

Geodesy

Answer 2

• is the determination & measurement of the Earth’s size , shape and figure in three- dimensional time-varying space.
• is primarily concerned with the geometric aspects and effects of temporal variations of gravity, polar motion, tides, and tectonics.
• defines and maintains the Terrestrial Reference Frame (geographic coordinate system, and horizontal and vertical datums) for precise 3D positioning.

Question 3

How do we know the Earth is not flat?

Answer 3

• Pythagoras (~580-500 BCE), Philosophically held the sphere as a perfect shape like the sun and moon. Held the earth must be spherical (2510-2590 y.o.).
• Aristotle and the ancient Greeks, held the earth as round, based on direct observations (N-S elevation differences of the stars, the fact that the day and night sky appeared somewhat different at different la8tudes, ships leaving port vanished hull first in whatever direction they traveled, lunar eclipses produced curved shadows on the moon)

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Question 4

Eratosthenes

Answer 4

He tested the Pythagoras’ and Aristotle’s hypothesis and made the first measurement of the ‘spherical’ circumference of the Earth.
 Produced one of the earliest maps of the Earth.
 Eratosthenes experiment:
 Alexandria is almost directly north of Syene.
 Alexandria to Syene sun angle is 7.5°, (1/50 of the total circumference of the Earth apart (7.5/360).
 estimated distance between the cities was 5000 stadia
 estimates a circumference of 252,000 stadia, or 39,690 km, an error of less than 1%. Radius estimated as ~6317 km, 3916 miles. 2250 years ago.

Question 5

Dantum

Answer 5

• is a set of reference points on the earth’s surface against which position measurements are made.
• It is often associated with a model of the shape of the earth (spheroid or ellipsoid) to define a geographic coordinate system.
• Horizontal datum describe a point on the earth’s surface in latitude and longitude, or a gridded coordinate system.
• Vertical datum measure elevations or depths.

Question 6

Latitude

Answer 6

of a point is the angle between the equatorial plane and a point whose line from the point drawn perpendicular to the ellipsoid surface. By convention, latitude is positive north of the equator, negative if south.

Question 7

Longitude

Answer 7

angle measured about the polar axis from a Prime Meridian plane, positive if east of 0° and negative if west. The zero longitude can be defined to be any meridian. By a 19th century the international convention put the standard Prime Meridian through Greenwich, England.

Question 8

Conventions for Latitude and Longitude:

Answer 8

• Degrees, Minutes, Seconds
• Degrees, Decimal Minutes
• Decimal Degrees

Question 9

Geographic Coordinate Systems (GCS)

Answer 9

• are based on a geodetic datums, projections, and units in use to give reference to locations on Earth. Polar coordinate systems use angles (azimuth, elevation) and length (vertical height).
• GCS with no projection-Spheroid, Ellipsoid and local systems
• Projected coordinate systems- Polar, UTM, State Plane

Question 10

Ellipsoidal Approximation

Answer 10

• 1666, the astronomer J.D. Cassini observed the flattening of the poles of Jupiter.
• The astronomer J. Richer in 1672, made pendulum observations at Cayenne, near the equator in South America, that indicated an increase of gravity from the equator to the poles.
• Issac Newton (1643-1727) and Christian Huygens (1629-1695) developed Earth models flattened at the poles based on the laws of motion and gravitation. Newton hypothesized that the Earth’s rotation creates a centrifugal effect which is strongest at the equator and zero at the poles implying an earth flattened at the poles, i.e., an oblate spheroid (ellipsoid of revolution). Polar axis is 21 km shorter than the Equatorial axis.

Question 11

A reference ellipsoid

Answer 11

• is modeled to be the same size (volume) as the Geoid of the Earth at “sea level”.
• It is described by its semi-major axis (equatorial radius) a, its semi-minor axis b, the polar radius.
• A flattening parameter f is a measure of the non- concentric-ness of the Earth. f= (a−b)/a.

Question 12

Conventional Terrestrial (CT) GCS System

Answer 12

• (called Reference Frames: NAD_83, WGS84, ITRF03, IGS08)
• Stationary, Earth-centered model.
• is a 3D Cartesian (X, Y, Z) system with its origin at the mass-center of the Earth.
• The Z axis = Earth’s Polar axis(semi-minor axis). The X-Z plane is the Mean Greenwich Zero Meridian, and the system is right handed. •
• The reference ellipsoid has an equatorial semi-major axis a and minor semi-axis b

Question 13

Ellipsoidal Approximation

Answer 13

Newton obtained a rotational ellipsoid as an equilibrium figure for a homogeneous, fluid, rotating earth based on the validity of the law of universal gravitation. The flattening, f,

Question 14

The triangulation surveys are carried out:

Answer 14

(i) to establish accurate control for plane and geode8c surveys of large areas. •
(ii) (ii) to establish accurate control for aerial lidar surveys of large areas •
(iii) to assist in the determina8on of the size and shape of the earth
(iv) to determine accurate loca8ons of points in engineering works