Geodetic Surveying: Aligning Local Astronomical Axes with Conventional Terrestrial Axes

When determining the position of a point on the Earth within a three-dimensional space, one method is to use the Conventional Terrestrial (CT) coordinate system: a Cartesian coordinate system with x, y, and z axes.

In this coordinate system,

• The origin (0,0,0) corresponds with the mass center of the earth.
• The X axis is parallel to the Equator and points through the Greenwich Meridian (0° longitude). The Greenwich Meridian is also known as the Prime Meridian.
• The Z axis is coincident to the conventional terrestrial pole (CTP) which was the mean position of the Earth's rotational axis between 1900 and 1905.
• The Y axis lies in the Earth's equatorial plane and is perpendicular to the X and Z axes and creates a right-handed Cartesian coordinate system.

The conventional terrestrial pole is commonly referred to as the Earth's North Pole.

Surveyors generally use a three-dimensional Cartesian system called the Local Astronomical (LA) coordinates to describe positions in reference to their own location.

In this coordinate system:

• The origin (0,0,0) corresponds with location of the instrument used to make surveying measurements on the surface of the Earth: from now on called the observer's station.
• The x axis (N) points from the origin towards the CTP (north) and is a tangent with the curvature of the Earth.
• The z axis (U) points away from the surface of the Earth opposite the direction of gravity towards the observer's zenith. Its negative axis points in the direction of gravity and the observer's nadir.
• The y axis (E) creates a left-handed Cartesian coordinate system by being perpendicular to both the x and z axes and pointing east from the observer's station. This axis is tangent to the curvature of the Earth at the observer's station.

Note that unless the observer is at the North Pole, the direction of the U axis (local astronomical z axis) will not align with the Z axis in the CT coordinate system.