/// <summary>
/// Evaluate the components of the acceleration due to gravity in geocentric coordinates.
/// </summary>
/// <param name="X">the <i>X</i> component of geocentric coordinate of point (meters).</param>
/// <param name="Y">the <i>Y</i> component of geocentric coordinate of point (meters).</param>
/// <param name="Z">the <i>Z</i> component of geocentric coordinate of point (meters).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>V</i> = <i>W</i> - Φ, the gravitational potential (m^2 s^−2).</item>
/// <item><i>GX</i>, the <i>X</i> component of the acceleration (m s^−2).</item>
/// <item><i>GY</i>, the <i>Y</i> component of the acceleration (m s^−2).</item>
/// <item><i>GZ</i>, the <i>Z</i> component of the acceleration (m s^−2).</item>
/// </list>
/// </returns>
public (double V, double GX, double GY, double GZ) V(double X, double Y, double Z)
{
double
Vres = _gravitational.Evaluate(X, Y, Z, out var GX, out var GY, out var GZ),
f = _GMmodel / _amodel;
Vres *= f;
GX *= f;
GY *= f;
GZ *= f;
return(Vres, GX, GY, GZ);
}
/// <summary>
/// Evaluate the geoid height.
/// </summary>
/// <param name="lat">the geographic latitude (degrees).</param>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <returns><i>N</i>, the height of the geoid above the <see cref="ReferenceEllipsoid"/> (meters).</returns>
/// <remarks>
/// This calls <see cref="NormalGravity.U(double, double, double)"/> for
/// <see cref="ReferenceEllipsoid"/>. Some approximations are made in computing the geoid height so that the results of
/// the NGA codes are reproduced accurately. Details are given in
/// <a href="https://geographiclib.sourceforge.io/html/gravity.html#gravitygeoid">Details of the geoid height and anomaly calculations</a>.
/// </remarks>
public double GeoidHeight(double lat, double lon)
{
var(X, Y, Z) = _earth.Earth.IntForward(lat, lon, 0);
double
gamma0 = _earth.SurfaceGravity(lat),
T = InternalT(X, Y, Z, out _, out _, out _, false, false),
invR = 1 / Hypot(Hypot(X, Y), Z),
correction = _corrmult * _correction.Evaluate(invR * X, invR * Y, invR * Z);
// _zeta0 has been included in _correction
return(T / gamma0 + correction);
}