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. This definition assumes Earth as a perfect sphere, considering all points on the surface to be equidistant from the center of the Earth. However, because Earth is actually an oblate spheroid, the geocentric latitude does not accurately reflect the surface curvature in terms of the actual distance from the equator or the poles.
The geodetic latitude μ on the Earth surface is defined by the angle between the equatorial plane and the normal to the reference ellipsoid that best approximates Earth's surface at that point. The reference ellipsoid has a smaller radius at the poles and a larger radius at the equator, matching Earth's shape more closely than a sphere would. Geodetic latitude is commonly used in mapping and navigation because it provides a more accurate representation of the location of a point on Earth's surface.
NED Coordinates
The north-east-down (NED) system is a noninertial system with its origin fixed at the center of gravity of the ground station, aircraft, or spacecraft. The NED axes are oriented along the geodetic directions defined by the Earth surface. The NED system is a type of local tangent plane coordinate system, which means it is defined relative to a specific location on Earth, defined by latitude, longitude and altitude, typically where the measurement is being made or the vehicle, such as an aircraft or drone, is operating.
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 outward normal n of the surface.
Flying at a constant altitude means flying at a constant
zabove the Earth's surface.
Local Vertical Local Horizontal (LVLH) coordinates
The LVLH (Local Vertical Local Horizontal) coordinate system is a rotating frame of reference that is defined relative to a primary body and is centered on a spacecraft or satellite in orbit.
The origin of the LVLH frame is the center of mass of the spacecraft or satellite. LVLH is a rotating, accelerating frame commonly used in studies of relative motion, such as vehicle maneuvering. The axes of this frame are:
R-axis — Points outward from the spacecraft origin along its position vectors (with respect to the center of Earth). Measurements along this axis are referred to as radial.
S-axis — Completes the right hand coordinate system. This axis points in the direction of the velocity vector, but is only parallel to it for circular orbits. Measurements along this axis are referred to as along-track or transverse.
W-axis — Points normal to the orbital plane. Measurements along this axis are referred to as cross-track.
