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 ecef_to_geodetic(r_e::AbstractVector)

which returns a tuple with:

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

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

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

julia> ecef_to_geodetic([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 geodetic_to_ecef(lat::Number, lon::Number, h::Number)

in which a 3x1 vector will be returned.

julia> geodetic_to_ecef(0,0,0)
3-element StaticArrays.SVector{3, Float64} with indices SOneTo(3):
 6.378137e6
 0.0
 0.0

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

Geocentric to Geodetic

Given a Geocentric latitude ϕ_gc [rad] and distance from the center of Earth r [m], one can obtain the Geodetic coordinates (Geodetic latitude and altitude above the reference ellipsoid - WGS84) using the following function:

function geocentric_to_geodetic(ϕ_gc::Number, r::Number)

in which a tuple with two values will be returned:

• The Geodetic latitude [rad]; and
• The altitude about the reference ellipsoid (WGS-84) [m].

julia> geocentric_to_geodetic(deg2rad(-22), R0)
(-0.3863099329112617, 3013.9291869809385)

julia> geocentric_to_geodetic(0, R0)
(0.0, 0.0)

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 geodetic_to_geocentric(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> geodetic_to_geocentric(deg2rad(-22), 0)
(-0.38164509973650357, 6.375157677217675e6)

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