Geometric Geodesy

  • What is the difference between a reference ellipsoid and a reference frame?
    • Reference ellipsoids
      • A reference ellipsoid is a simple geometric model of the shape and the size of a celestial body, notably, the Earth. Earth is nearly spherical, but its polar axis is slightly shorter than its Equatorial axis by about one part in 298. Therefore, reference ellipsoids are, as the name suggests, ellipsoids of revolution, meaning the shape that results from spinning an ellipse around, in this case, its semi-minor axis.
      • The two modern reference ellipsoids are named the Global Reference System of 1980 (GRS 80) and the World Geodetic System 1984 (WGS 84).
      • Reference ellipsoids are realistic in that they are intended to be accurate models of Earth’s general shape and size.
      • Reference ellipsoids are not real in that they don’t actually physically exist. They are mathematical models, nothing more.
    • Reference frames
      • A reference frame is an actual, physical system that allows the locations of places-of-interest to be given spatial coordinates, like longitude, latitude, and height.
      • In the past, surveyors would access a reference frame (then called a datum) by recovering passive survey control markers from which to base a survey. Nowadays, it is more common to access a reference frame using global navigation satellite system (GNSS) positioning technologies.
      • Modern reference frames create Cartesian XYZ coordinate systems whose
        • origin is at Earth’s center of mass (as best known when the reference frame was created)
        • Z-axis is nominally parallel and close to Earth’s rotational axis on average
        • X-axis is perpendicular to the Z-axis, going through the center of the Earth
        • Y-axis is perpendicular to both the X- and Z-axes, forming a right-handed coordinate system.
    • The XZ plane defines the location of the Prime Meridian
    • The XY plane defines the location of the Equator.
  • Reference frames and reference ellipsoids
    • Modern reference frames place a reference ellipsoid such that the reference ellipsoid’s center is at the reference frame’s origin at the center of the Earth.
    • The role of a reference ellipsoid, nowadays, is to provide the parameters for the formulas that convert from geodetic longitude, latitude, and height to-and-from X, Y, and Z coordinates.

Physical Geodesy