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Coordinate Systems for Navigation

Modeling aerospace trajectories requires positioning and orienting the aircraft or spacecraft with respect to the rotating Earth. Navigation coordinates are defined with respect to the center and surface of the Earth.

Geocentric and Geodetic Latitudes

The geocentric latitude λ on the Earth surface is defined by the angle subtended by the radius vector from the Earth center to the surface point with the equatorial plane.

The geodetic latitude μ on the Earth surface is defined by the angle subtended by the surface normal vector n and the equatorial plane.

NED Coordinates

The north-east-down (NED) system is a noninertial system with its origin fixed at the aircraft or spacecraft's center of gravity. Its axes are oriented along the geodetic directions defined by the Earth surface.

  • The x-axis points north parallel to the geoid surface, in the polar direction.

  • The y-axis points east parallel to the geoid surface, along a latitude curve.

  • The z-axis points downward, toward the Earth surface, antiparallel to the surface's outward normal n.

    Flying at a constant altitude means flying at a constant z above the Earth's surface.

ECI Coordinates

The Earth-centered inertial (ECI) system is a mixed inertial system. It is oriented with respect to the Sun. Its origin is fixed at the center of the Earth.

  • The z-axis points northward along the Earth's rotation axis.

  • The x-axis points outward in the Earth's equatorial plane exactly at the Sun. (This rule ignores the Sun's oblique angle to the equator, which varies with season. The actual Sun always remains in the x-z plane.)

  • The y-axis points into the eastward quadrant, perpendicular to the x-z plane so as to satisfy the RH rule.

Earth-Centered Coordinates

ECEF Coordinates

The Earth-center, Earth-fixed (ECEF) system is a noninertial system that rotates with the Earth. Its origin is fixed at the center of the Earth.

  • The z-axis points northward along the Earth's rotation axis.

  • The x-axis points outward along the intersection of the Earth's equatorial plane and prime meridian.

  • The y-axis points into the eastward quadrant, perpendicular to the x-z plane so as to satisfy the RH rule.