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geod2geoc

Convert geodetic latitude to geocentric latitude

Syntax

geocentricLatitude = geod2geoc(geodeticLatitude,height)
[geocentricLatitude,radii] = geod2geoc(geodeticLatitude,height)
geocentricLatitude = geod2geoc(geodeticLatitude,height,model)
[geocentricLatitude,radii] = geod2geoc(geodeticLatitude,height,model)
geocentricLatitude = geod2geoc(geodeticLatitude,height,flattening,equatorialRadius)
[geocentricLatitude,radii] = geod2geoc(geodeticLatitude,height,flattening,equatorialRadius)

Description

geocentricLatitude = geod2geoc(geodeticLatitude,height) and [geocentricLatitude,radii] = geod2geoc(geodeticLatitude,height) convert an array of geodetic latitudes, geodeticLatitude, and an array of mean sea level altitudes, height, into an array of geocentric latitudes, geocentricLatitude. The optional radii returns the radius from the center of the planet to the center of gravity.

geocentricLatitude = geod2geoc(geodeticLatitude,height,model) and [geocentricLatitude,radii] = geod2geoc(geodeticLatitude,height,model) convert from geodetic to geocentric latitude for a specific ellipsoid planet.

geocentricLatitude = geod2geoc(geodeticLatitude,height,flattening,equatorialRadius) and [geocentricLatitude,radii] = geod2geoc(geodeticLatitude,height,flattening,equatorialRadius) convert from geodetic to geocentric latitude for a custom ellipsoid planet defined by flattening, flattening, and the equatorial radius, equatorialRadius.

Input Arguments

geodeticLatitude

Array of geodetic latitudes, in degrees.

height

Scalar of mean sea-level altitude (MSL), in meters.

model

Specific ellipsoid planet. This function supports only 'WGS84'.

flattening

Custom ellipsoid planet defined by flattening.

equatorialRadius

Equatorial radius, in meters.

Output Arguments

geocentricLatitude

Array of geocentric latitudes, in degrees. Latitude values can be any value. However, values of +90 and -90 may return unexpected values because of singularity at the poles.

radii

Array of radii from the center of the planet, in meters.

Examples

Determine geocentric latitude given a geodetic latitude and altitude:

[gc,r] = geod2geoc(45,1000)
gc =
   44.8076

r =
   6.3685e+06

Determine geocentric latitude at multiple geodetic latitudes and altitudes, specifying WGS84 ellipsoid model:

[gc,r] = geod2geoc([0 45 90],[1000 0 2000],'WGS84')
gc =
         0   44.8076   90.0000

r =
   1.0e+06 *
    6.3791    6.3675    6.3588

Determine geocentric latitude at multiple geodetic latitudes, given an altitude and specifying custom ellipsoid model:

f = 1/196.877360;
Re = 3397000;
[gc,r] = geod2geoc([0 45 90],2000,f,Re)
gc =
         0   44.7084   90.0000

r =
   1.0e+06 *
    3.3990    3.3904    3.3817

Assumptions and Limitations

This implementation generates a geocentric latitude that lies between ±90 degrees.

References

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, NY, 1992

Introduced in R2006b