Geodetic and Geocentric

There are three functions that can help to convert between geodetic and geocentric representations. Notice that currently all Geodetic representations are based on the WGS84 reference ellipsoid.

ECEF to Geodetic

It is possible to convert a position vector represented in an Earth-Centered, Earth-Fixed frame (ECEF) r_e to the Geodetic latitude, longitude, and altitude by the following function:

function ECEFtoGeodetic(r_e::AbstractVector)

which returns a tuple with:

• The Geocentric latitude [rad];
• The longitude [rad]; and
• The altitude above the reference ellipsoid [m].

julia> ECEFtoGeodetic([R0;0;0])
(0.0, 0.0, 0.0)

julia> ECEFtoGeodetic([0;R0;0])
(0.0, 1.5707963267948966, 0.0)

julia> ECEFtoGeodetic([0;0;R0])
(1.5707963267948966, 0.0, 21384.685754820704)

Geodetic to ECEF

The Geodetic latitude lat [rad], longitude lon [rad], and altitude h [m] can be converted to a vector represented in an ECEF reference frame by the following function:

function GeodetictoECEF(lat::Number, lon::Number, h::Number)

in which a 3x1 vector will be returned.

julia> GeodetictoECEF(0,0,0)
3-element StaticArrays.SArray{Tuple{3},Float64,1,3} with indices SOneTo(3):
 6.378137e6
 0.0
 0.0

julia> GeodetictoECEF(deg2rad(-22),deg2rad(-45),0)
3-element StaticArrays.SArray{Tuple{3},Float64,1,3} with indices SOneTo(3):
  4.1835869067109847e6
 -4.1835869067109837e6
 -2.3744128953028163e6

Geodetic to Geocentric

Given a Geodetic latitude ϕ_gd [rad] and altitude above the reference ellipsoid h [m], one can obtain the Geocentric coordinates (Geocentric latitude and position from the center of Earth) using the following function:

function GeodetictoGeocentric(ϕ_gd::Number, h::Number)

in which a tuple with two values will be returned:

• The Geocentric latitude [rad]; and
• The distance from the center of Earth [m].

julia> GeodetictoGeocentric(deg2rad(-22), 0)
(-0.38164509973650357, 6.375157677217675e6)

julia> GeodetictoGeocentric(0,0)
(0.0, 6.378137e6)