Coordinates and Geodesy
Jan Van Sickle 1. Which of the following coordinate systems express each position with distances without angles?
a) Latitude and Longitude b) Cartesian coordinates c) Polar Coordinates d) None of the above 2. Presuming that all numbers to the right of the decimal are significant, which value below is nearest to the precision of the following coordinates?
= 6014’15.3278”N λ = 14954’11.1457”W
a) 10.0 FT. b) 1.0 FT. c) 0.10 FT. d) 0.01 FT. 3. Which of the following statements about two- dimensional Cartesian coordinates is incorrect?
a) Universal Transverse Mercator coordinates are Cartesian coordinates.
b) Most Cartesian coordinate systems are designed to place all coordinates in the first quadrant.
c) Cartesian coordinates derived from positions on the Earth always include distortion.
d) Directions in Cartesian coordinate systems are always reckoned from north. 4. Which of the following statements about latitude is not true?
a) The geocentric latitude of a point is usually smaller than the geodetic latitude of the same point.
b) Geodetic latitude is not derived from direct measurement with optical instruments.
c) The astronomic latitude is usually quite close to the geodetic latitude of the same point.
d) The geodetic latitude of a point remains constant despite datum shifts. 5. As one proceeds northward from the equator, which of the following does not happen? a) Meridians converge b) Latitudinal lines are parallel c) The force of gravity increases d) The distance represented by a degree of latitude gets shorter 6. Presuming that all numbers to the right of the decimal are significant, which value below is nearest to the precision of the following coordinates?
= 6014’15.3278”N λ = 14954’11.1457”W
a) 10.0 FT. b) 1.0 FT. c) 0.10 FT. d) 0.01 FT. 7. Which of the following coordinate systems express each position with an angle and a distance?
a) Latitude and Longitude b) Cartesian coordinates c) Polar Coordinates d) None of the above 8. Which of the following correctly describes a characteristic both Cartesian coordinates and polar coordinates share? a) Each point has only one unique coordinate pair b) Coordinates are expressed in ordered pairs c) Angles are measured clockwise from north in degrees, minutes and seconds d) Coordinates are always positive 9. Which of the following statements concerning the deflection of the vertical is correct?
a) The deflection of the vertical is comprised of the north-south and east-west components of the difference between the geodetic and geocentric latitude and longitude of a point.
b) The deflection of the vertical at a point can be derived from astronomic observations alone.
c) The deflection of the vertical at a point can be derived from geodetic coordinates alone.
d) The deflection of the vertical is used in the conversion of astronomic coordinates and astronomic directions to their geodetic counterparts and vice versa. 10. Which of the following statements is not correct concerning the figure of an oblate spheroid?
a) It is an ellipsoid of revolution rotated about its shorter axis. b) It is flattened at the poles c) Its minor axis is in the equatorial plane. d) It is a good representation of the general shape of the Earth 11. Which of the following pairs of parameters is not usually used to define a reference ellipsoid?
a) the semimajor and semiminor axes b) the semimajor axis and the reciprocal of the flattening c) the semimajor axis and the eccentricity. d) the semimajor axis and the reciprocal of the eccentricity. 12. Which of the following is the reference ellipsoid for North American Datum 1983?
a) OSGB36 b) GRS80 c) WGS66 d) ITRF88 13. Which of the following is the reference ellipsoid for NAD27?
a) Clarke 1858 b) Bessel 1841 c) Clarke 1866 d) Clarke 1880 15. Which of the following acronyms identifies a realization of the International Terrestrial Reference System?
a) VLBI b) SLR c) ITRF88 d) IERS 18. Which of the following heights is not measured along a line that is perpendicular to the ellipsoid?
a) An ellipsoidal height b) A geoid height c) A geodetic height d) An orthometric height 19. Which of the following are the same?
a) ellipsoidal height and dynamic height b) geodetic height and orthometric height c) orthometric height and ellipsoidal height d) ellipsoidal height and geodetic height 20. Which of the following coordinate systems express each position with angles without distances?
a) Latitude and Longitude b) Cartesian coordinates c) Polar Coordinates d) None of the above 21. Which of these values would not have been affected by gravity?
a) An ellipsoidal height of 2729.463 meters b) 983.124 gals from a gravimeter measurement c) The measurement of hourly heights of the sea at a primary-control tide station d) An orthometric elevation of 5176.00 feet derived from spirit leveling 22. When the heights of benchmarks from a spirit level circuit are compared with the orthometric heights of the same benchmarks calculated from GPS observations they may differ even though they both are based on NAVD88. Which of the following could not contribute to the difference?
a) The undulation of the GRS80 ellipsoid.
b) Lack of balance between the foresights and the backsights when the spirit level circuit was run.
c) Error in the geoid height calculated from GEOID99.
d) The lack of parallelism in equipotential surfaces. 23. Which of the following statements is correct?
a) In the coterminous United States the GRS80 ellipsoid is always below the geoid that best fits Mean Sea Level per least squares.
b) The heights of the Atlantic Ocean and the Pacific Ocean are the same
c) Mean Sea Level and the geoid that best fits Mean Sea Level from a least squares point of view nevertheless deviates from Mean Sea Level up to 2 meters at some places.
d) The geoid that best fits Mean Sea Level from a least squares point of view is always below the GRS80 ellipsoid all around the world. 24. Which of the following formulae correctly represents the basic relationship between geodetic, geoid and orthometric heights?
a) H = h+N b) h = H+N c) N = H+h d) None of the above 25. Until the 1940’s the Coast and Geodetic Survey stamped the elevation of a point on its monuments. In what sense would those elevations be obsolete now?
a) They would be expressed in feet, not in meters b) The elevations would be based on the Clarke reference ellipsoid c) The elevations would not be in the North American Datum of 1988 d) The elevations would be dynamic rather than orthometric 26. Which of the following general statements about the State Plane Coordinate systems in the United States is incorrect?
a) There are three map projections used in SPCS in the US.
b) The map projections used in the SPCS cause meridians of longitude to appear as straight lines on the SPCS grid.
c) Some states utilize more than one map projection in their SPCS.
d) The axis of the Lambert cone is coincident with the Earth’s polar axis; the axis of the Transverse Mercator cylinder is perpendicular to it. 27. Which of the following map projections is used as the basis of SPCS in the United States?
a) The Lambert projection. b) The Transverse Mercator projection c) The Oblique Mercator projection d) a,b and c 28. Which of the following statements describes the treatment of scale in the Lambert and Transverse Mercator projections? a) The Lambert projection is variable with respect to the changes in longitude; in the Transverse Mercator projection, it varies with respect to latitude.
b) In the Transverse Mercator projection, the lines of exact scale are meridians of longitude; in the Lambert projection, they are called standard parallels of latitude.
c) The Transverse Mercator projections used as the foundation of SPCS are designed to limit scale distortion to 1 part in 20,000; in Lambert- based systems, distortion is limited to 1 part in 10,000.
d) The scale is constant up and down the central meridian of a Transverse Mercator projection; it is variable along the central meridian of a Lambert projection. 29. Which of the following statements correctly describes an aspect of conformal map projection in SPCS?
a) It ensures that the angle between two lines on the map projection surface is the same as it is on the reference ellipsoid regardless of their length.
b) In a conformal map projection the scale is the same in all directions from a point.
c) Convergence in a conformal map projection is always much less than 1°.
d) The Lambert Conic projection is a conformal projection but the Transverse Mercator projection is not. 30. Many SPCS systems are designed to limit scale distortion to 1 part in 10,000. If this goal has been achieved, within what limits should the scale factor fall?
a) Not less than 0.9999823 and not more than 1.0001787 b) Not less than 0.9999569 and not more than 1.0000839 c) Not less than 0.9999000 and not more than 1.0001000 d) Not less than 0.9994563 and not more than 1.0051020 31. Which of the following statements about the scale factor in SPCS is true?
a) The scale factor changes constantly along the central meridian of a Transverse Mercator SPCS zone.
b) Scale factor ratios are 1 part in 10,000 in SPCS zones.
c) A scale factor is used in SPCS to convert a length on the reference ellipsoid to a length on the map projection plane grid.
d) The scale factor does not change along the central meridian of a Lambert Conic SPCS zone. 32. The combined factor is used in SPCS conversion. How is the combined factor calculated?
a) The scale factor is multiplied by the elevation factor b) The scale factor is divided by the grid factor c) The grid factor added to the elevation factor and the sum is divided by two d) The scale factor is multiplied by the grid factor 33. Which of the following statements does not properly describe a change in the State Plane Coordinate Systems from SPCS27 to SPCS83?
a) There have been changes in the distances between the SPCS zones and their origins.
b) SPCS83 coordinates are expressed in more units than were SPCS27 coordinates.
c) There are fewer SPCS83 zones than there were SPCS27 zones in some states.
d) In SPCS83 the scale factor limit of 1 part in 10,000 has been exceeded for the first time. 34. Which of the following statements about convergence angles in SPCS is not correct?
a) As the distance from the central meridian increases, the absolute values of the convergence angles increase.
b) As the length of a line connecting two stations increases, the absolute values of the convergence angles at each end station increase.
c) As the direction of a line connecting two stations approaches cardinal, north-south or east-west, the absolute values of the convergence angles at each end station are not affected.
d) As the latitude decreases, the absolute values of the convergence angles decrease. 35. If a line on a secant map projection plane crossed one of the standard lines, what would be the difference between the scale factor at the end between the standard lines and the scale factor at the end outside the standard lines? a) The scale factor at the station outside the standard lines would be greater than 1, the scale factor for the station between the standard lines would be less than 1.
b) For an east-west line that crossed a standard parallel in a Lambert Conic projection the scale would be the same at both ends of the line.
c) For a north-south line that crossed a standard line of exact scale in a Transverse Mercator projection the scale would be the same at both ends of the line.
d) The scale factor at the station outside the standard lines would be less than 1, the scale factor for the station between the standard lines would be greater than 1. 36. Which of the following does not correctly state a difference between the Transverse Mercator coordinate system used in SPCS and the Universal Transverse Mercator coordinate system? a) The UTM system of coordinates was designed and established by the United State Army in cooperation with NATO member nations. The Transverse Mercator SPCS was established by the United States Coast and Geodetic Survey. b) The official unit of measurement in UTM system of coordinates is the meter. The official unit in Transverse Mercator SPCS83 is the International foot. c) The UTM system of coordinates is augmented by UPS to complete its worldwide coverage. The Transverse Mercator SPCS does not have such a broad scope. d) The scale factor in the UTM system of coordinates can reach 1 part in 2,500. In the Transverse Mercator SPCS the scale factor is usually no more than 1 part in 10,000.