Model of the earth's gravity field. More...

#include <GeographicLib/GravityModel.hpp>

Public Types
enum	mask { NONE , GRAVITY , DISTURBANCE , DISTURBING_POTENTIAL , SPHERICAL_ANOMALY , GEOID_HEIGHT , ALL }

Public Member Functions
Setting up the gravity model
	GravityModel (const std::string &name, const std::string &path="", int Nmax=-1, int Mmax=-1)

Compute gravity in geodetic coordinates
Math::real	Gravity (real lat, real lon, real h, real &gx, real &gy, real &gz) const

Math::real	Disturbance (real lat, real lon, real h, real &deltax, real &deltay, real &deltaz) const

Math::real	GeoidHeight (real lat, real lon) const

void	SphericalAnomaly (real lat, real lon, real h, real &Dg01, real &xi, real &eta) const

Compute gravity in geocentric coordinates
Math::real	W (real X, real Y, real Z, real &gX, real &gY, real &gZ) const

Math::real	V (real X, real Y, real Z, real &GX, real &GY, real &GZ) const

Math::real	T (real X, real Y, real Z, real &deltaX, real &deltaY, real &deltaZ) const

Math::real	T (real X, real Y, real Z) const

Math::real	U (real X, real Y, real Z, real &gammaX, real &gammaY, real &gammaZ) const

Math::real	Phi (real X, real Y, real &fX, real &fY) const

Compute gravity on a circle of constant latitude
GravityCircle	Circle (real lat, real h, unsigned caps=ALL) const

Inspector functions
const NormalGravity &	ReferenceEllipsoid () const

const std::string &	Description () const

const std::string &	DateTime () const

const std::string &	GravityFile () const

const std::string &	GravityModelName () const

const std::string &	GravityModelDirectory () const

Math::real	EquatorialRadius () const

Math::real	MassConstant () const

Math::real	ReferenceMassConstant () const

Math::real	AngularVelocity () const

Math::real	Flattening () const

int	Degree () const

int	Order () const

Static Public Member Functions
static std::string	DefaultGravityPath ()

static std::string	DefaultGravityName ()

Friends
class	GravityCircle

Detailed Description

Model of the earth's gravity field.

Evaluate the earth's gravity field according to a model. The supported models treat only the gravitational field exterior to the mass of the earth. When computing the field at points near (but above) the surface of the earth a small correction can be applied to account for the mass of the atmosphere above the point in question; see The effect of the mass of the atmosphere. Determining the height of the geoid above the ellipsoid entails correcting for the mass of the earth above the geoid. The egm96 and egm2008 include separate correction terms to account for this mass.

Definitions and terminology (from Heiskanen and Moritz, Sec 2-13):

V = gravitational potential;
Φ = rotational potential;
W = V + Φ = T + U = total potential;
V₀ = normal gravitation potential;
U = V₀ + Φ = total normal potential;
T = W − U = V − V₀ = anomalous or disturbing potential;
g = ∇W = γ + δ;
f = ∇Φ;
Γ = ∇V₀;
γ = ∇U;
δ = ∇T = gravity disturbance vector = g_P − γ_P;
δg = gravity disturbance = g_P − γ_P;
Δg = gravity anomaly vector = g_P − γ_Q; here the line PQ is perpendicular to ellipsoid and the potential at P equals the normal potential at Q;
Δg = gravity anomaly = g_P − γ_Q;
(ξ, η) deflection of the vertical, the difference in directions of g_P and γ_Q, ξ = NS, η = EW.
X, Y, Z, geocentric coordinates;
x, y, z, local cartesian coordinates used to denote the east, north and up directions.

See Gravity models for details of how to install the gravity models and the data format.

References:

W. A. Heiskanen and H. Moritz, Physical Geodesy (Freeman, San Francisco, 1967).

Example of use:

// Example of using the GeographicLib::GravityModel class
// This requires that the egm96 gravity model be installed; see
// https://geographiclib.sourceforge.io/C++/doc/gravity.html#gravityinst
 
#include <iostream>
#include <exception>
#include <GeographicLib/GravityModel.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  try {
    GravityModel grav("egm96");
    double lat = 27.99, lon = 86.93, h = 8820; // Mt Everest
    double gx, gy, gz;
    grav.Gravity(lat,lon, h, gx, gy, gz);
    cout << gx << " " << gy << " " << gz << "\n";
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

Gravity is a command-line utility providing access to the functionality of GravityModel and GravityCircle.

Definition at line 83 of file GravityModel.hpp.

Member Enumeration Documentation

◆ mask

enum GeographicLib::GravityModel::mask

Bit masks for the capabilities to be given to the GravityCircle object produced by Circle.

Enumerator
NONE	No capabilities.
GRAVITY	Allow calls to GravityCircle::Gravity, GravityCircle::W, and GravityCircle::V.
DISTURBANCE	Allow calls to GravityCircle::Disturbance and GravityCircle::T.
DISTURBING_POTENTIAL	Allow calls to GravityCircle::T(real lon) (i.e., computing the disturbing potential and not the gravity disturbance vector).
SPHERICAL_ANOMALY	Allow calls to GravityCircle::SphericalAnomaly.
GEOID_HEIGHT	Allow calls to GravityCircle::GeoidHeight.
ALL	All capabilities.

Definition at line 123 of file GravityModel.hpp.

Constructor & Destructor Documentation

◆ GravityModel()

GeographicLib::GravityModel::GravityModel	(	const std::string &	name,
		const std::string &	path = `""`,
		int	Nmax = `-1`,
		int	Mmax = `-1`
	)

explicit

Construct a gravity model.

Parameters

[in]	name	the name of the model.
[in]	path	(optional) directory for data file.
[in]	Nmax	(optional) if non-negative, truncate the degree of the model this value.
[in]	Mmax	(optional) if non-negative, truncate the order of the model this value.

Exceptions

GeographicErr	if the data file cannot be found, is unreadable, or is corrupt, or if Mmax > Nmax.
std::bad_alloc	if the memory necessary for storing the model can't be allocated.

A filename is formed by appending ".egm" (World Gravity Model) to the name. If path is specified (and is non-empty), then the file is loaded from directory, path. Otherwise the path is given by DefaultGravityPath().

This file contains the metadata which specifies the properties of the model. The coefficients for the spherical harmonic sums are obtained from a file obtained by appending ".cof" to metadata file (so the filename ends in ".egm.cof").

If Nmax ≥ 0 and Mmax < 0, then Mmax is set to Nmax. After the model is loaded, the maximum degree and order of the model can be found by the Degree() and Order() methods.

Definition at line 38 of file GravityModel.cpp.

References GeographicLib::SphericalHarmonic::Coefficients(), DefaultGravityPath(), GeographicLib::NormalGravity::MassConstant(), GeographicLib::SphericalEngine::coeff::mmx(), GeographicLib::SphericalEngine::coeff::N(), GeographicLib::SphericalEngine::coeff::nmx(), GeographicLib::SphericalEngine::coeff::readcoeffs(), and GeographicLib::Math::sq().

Member Function Documentation

◆ Gravity()

Math::real GeographicLib::GravityModel::Gravity	(	real	lat,
		real	lon,
		real	h,
		real &	gx,
		real &	gy,
		real &	gz
	)		const

Evaluate the gravity at an arbitrary point above (or below) the ellipsoid.

Parameters

[in]	lat	the geographic latitude (degrees).
[in]	lon	the geographic longitude (degrees).
[in]	h	the height above the ellipsoid (meters).
[out]	gx	the easterly component of the acceleration (m s⁻²).
[out]	gy	the northerly component of the acceleration (m s⁻²).
[out]	gz	the upward component of the acceleration (m s⁻²); this is usually negative.

Returns: W the sum of the gravitational and centrifugal potentials (m² s⁻²).

The function includes the effects of the earth's rotation.

Definition at line 304 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Earth(), and W().

Referenced by main().

◆ Disturbance()

Math::real GeographicLib::GravityModel::Disturbance	(	real	lat,
		real	lon,
		real	h,
		real &	deltax,
		real &	deltay,
		real &	deltaz
	)		const

Evaluate the gravity disturbance vector at an arbitrary point above (or below) the ellipsoid.

Parameters

[in]	lat	the geographic latitude (degrees).
[in]	lon	the geographic longitude (degrees).
[in]	h	the height above the ellipsoid (meters).
[out]	deltax	the easterly component of the disturbance vector (m s⁻²).
[out]	deltay	the northerly component of the disturbance vector (m s⁻²).
[out]	deltaz	the upward component of the disturbance vector (m s⁻²).

Returns: T the corresponding disturbing potential (m² s⁻²).

Definition at line 312 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Earth().

Referenced by main().

◆ GeoidHeight()

Math::real GeographicLib::GravityModel::GeoidHeight	(	real	lat,
		real	lon
	)		const

Evaluate the geoid height.

Parameters

[in]	lat	the geographic latitude (degrees).
[in]	lon	the geographic longitude (degrees).

Returns: N the height of the geoid above the ReferenceEllipsoid() (meters).

This calls NormalGravity::U for 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 Details of the geoid height and anomaly calculations.

Definition at line 290 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Earth(), GeographicLib::NormalGravity::SurfaceGravity(), and T().

Referenced by main().

◆ SphericalAnomaly()

void GeographicLib::GravityModel::SphericalAnomaly	(	real	lat,
		real	lon,
		real	h,
		real &	Dg01,
		real &	xi,
		real &	eta
	)		const

Evaluate the components of the gravity anomaly vector using the spherical approximation.

Parameters

[in]	lat	the geographic latitude (degrees).
[in]	lon	the geographic longitude (degrees).
[in]	h	the height above the ellipsoid (meters).
[out]	Dg01	the gravity anomaly (m s⁻²).
[out]	xi	the northerly component of the deflection of the vertical (degrees).
[out]	eta	the easterly component of the deflection of the vertical (degrees).

The spherical approximation (see Heiskanen and Moritz, Sec 2-14) is used so that the results of the NGA codes are reproduced accurately. approximations used here. Details are given in Details of the geoid height and anomaly calculations.

Definition at line 264 of file GravityModel.cpp.

References GeographicLib::Math::degree(), GeographicLib::NormalGravity::Earth(), T(), and GeographicLib::NormalGravity::U().

Referenced by main().

◆ W()

Math::real GeographicLib::GravityModel::W	(	real	X,
		real	Y,
		real	Z,
		real &	gX,
		real &	gY,
		real &	gZ
	)		const

Evaluate the components of the acceleration due to gravity and the centrifugal acceleration in geocentric coordinates.

Parameters

[in]	X	geocentric coordinate of point (meters).
[in]	Y	geocentric coordinate of point (meters).
[in]	Z	geocentric coordinate of point (meters).
[out]	gX	the X component of the acceleration (m s⁻²).
[out]	gY	the Y component of the acceleration (m s⁻²).
[out]	gZ	the Z component of the acceleration (m s⁻²).

Returns: W = V + Φ the sum of the gravitational and centrifugal potentials (m² s⁻²).

This calls NormalGravity::U for ReferenceEllipsoid().

Definition at line 255 of file GravityModel.cpp.

References GeographicLib::NormalGravity::Phi(), and V().

Referenced by Gravity().

◆ V()

Math::real GeographicLib::GravityModel::V	(	real	X,
		real	Y,
		real	Z,
		real &	GX,
		real &	GY,
		real &	GZ
	)		const

Evaluate the components of the acceleration due to gravity in geocentric coordinates.

Parameters

[in]	X	geocentric coordinate of point (meters).
[in]	Y	geocentric coordinate of point (meters).
[in]	Z	geocentric coordinate of point (meters).
[out]	GX	the X component of the acceleration (m s⁻²).
[out]	GY	the Y component of the acceleration (m s⁻²).
[out]	GZ	the Z component of the acceleration (m s⁻²).

Returns: V = W - Φ the gravitational potential (m² s⁻²).

Definition at line 243 of file GravityModel.cpp.

Referenced by W().

◆ T() [1/2]

Math::real GeographicLib::GravityModel::T	(	real	X,
		real	Y,
		real	Z,
		real &	deltaX,
		real &	deltaY,
		real &	deltaZ
	)		const

inline

Evaluate the components of the gravity disturbance in geocentric coordinates.

Parameters

[in]	X	geocentric coordinate of point (meters).
[in]	Y	geocentric coordinate of point (meters).
[in]	Z	geocentric coordinate of point (meters).
[out]	deltaX	the X component of the gravity disturbance (m s⁻²).
[out]	deltaY	the Y component of the gravity disturbance (m s⁻²).
[out]	deltaZ	the Z component of the gravity disturbance (m s⁻²).

Returns: T = W - U the disturbing potential (also called the anomalous potential) (m² s⁻²).

Definition at line 337 of file GravityModel.hpp.

Referenced by GeoidHeight(), and SphericalAnomaly().

◆ T() [2/2]

Math::real GeographicLib::GravityModel::T	(	real	X,
		real	Y,
		real	Z
	)		const

inline

Evaluate disturbing potential in geocentric coordinates.

Parameters

[in]	X	geocentric coordinate of point (meters).
[in]	Y	geocentric coordinate of point (meters).
[in]	Z	geocentric coordinate of point (meters).

Returns: T = W - U the disturbing potential (also called the anomalous potential) (m² s⁻²).

Definition at line 350 of file GravityModel.hpp.

◆ U()

Math::real GeographicLib::GravityModel::U	(	real	X,
		real	Y,
		real	Z,
		real &	gammaX,
		real &	gammaY,
		real &	gammaZ
	)		const

inline

Evaluate the components of the acceleration due to normal gravity and the centrifugal acceleration in geocentric coordinates.

Parameters

[in]	X	geocentric coordinate of point (meters).
[in]	Y	geocentric coordinate of point (meters).
[in]	Z	geocentric coordinate of point (meters).
[out]	gammaX	the X component of the normal acceleration (m s⁻²).
[out]	gammaY	the Y component of the normal acceleration (m s⁻²).
[out]	gammaZ	the Z component of the normal acceleration (m s⁻²).

Returns: U = V₀ + Φ the sum of the normal gravitational and centrifugal potentials (m² s⁻²).

This calls NormalGravity::U for ReferenceEllipsoid().

Definition at line 374 of file GravityModel.hpp.

References GeographicLib::NormalGravity::U().

◆ Phi()

Math::real GeographicLib::GravityModel::Phi	(	real	X,
		real	Y,
		real &	fX,
		real &	fY
	)		const

inline

Evaluate the centrifugal acceleration in geocentric coordinates.

Parameters

[in]	X	geocentric coordinate of point (meters).
[in]	Y	geocentric coordinate of point (meters).
[out]	fX	the X component of the centrifugal acceleration (m s⁻²).
[out]	fY	the Y component of the centrifugal acceleration (m s⁻²).

Returns: Φ the centrifugal potential (m² s⁻²).

This calls NormalGravity::Phi for ReferenceEllipsoid().

Definition at line 392 of file GravityModel.hpp.

References GeographicLib::NormalGravity::Phi().

◆ Circle()

GravityCircle GeographicLib::GravityModel::Circle	(	real	lat,
		real	h,
		unsigned	caps = `ALL`
	)		const

Create a GravityCircle object to allow the gravity field at many points with constant lat and h and varying lon to be computed efficiently.

Parameters

[in]	lat	latitude of the point (degrees).
[in]	h	the height of the point above the ellipsoid (meters).
[in]	caps	bitor'ed combination of GravityModel::mask values specifying the capabilities of the resulting GravityCircle object.

Exceptions

std::bad_alloc if the memory necessary for creating a GravityCircle can't be allocated.

Returns: a GravityCircle object whose member functions computes the gravitational field at a particular values of lon.

The GravityModel::mask values are

caps |= GravityModel::GRAVITY
caps |= GravityModel::DISTURBANCE
caps |= GravityModel::DISTURBING_POTENTIAL
caps |= GravityModel::SPHERICAL_ANOMALY
caps |= GravityModel::GEOID_HEIGHT

The default value of caps is GravityModel::ALL which turns on all the capabilities. If an unsupported function is invoked, it will return NaNs. Note that GravityModel::GEOID_HEIGHT will only be honored if h = 0.

If the field at several points on a circle of latitude need to be calculated then creating a GravityCircle object and using its member functions will be substantially faster, especially for high-degree models. See Geoid heights on a multi-processor system for an example of using GravityCircle (together with OpenMP) to speed up the computation of geoid heights.

Definition at line 322 of file GravityModel.cpp.

References GeographicLib::SphericalHarmonic::Circle(), GeographicLib::SphericalHarmonic1::Circle(), GeographicLib::NormalGravity::Earth(), GravityCircle, GeographicLib::Math::NaN(), GeographicLib::NormalGravity::Phi(), GeographicLib::NormalGravity::SurfaceGravity(), and GeographicLib::NormalGravity::U().

Referenced by main().

◆ ReferenceEllipsoid()

const NormalGravity & GeographicLib::GravityModel::ReferenceEllipsoid ( ) const

inline

Returns: the NormalGravity object for the reference ellipsoid.

Definition at line 441 of file GravityModel.hpp.

◆ Description()

const std::string & GeographicLib::GravityModel::Description ( ) const

inline

Returns: the description of the gravity model, if available, in the data file; if absent, return "NONE".

Definition at line 447 of file GravityModel.hpp.

Referenced by main().

◆ DateTime()

const std::string & GeographicLib::GravityModel::DateTime ( ) const

inline

Returns: date of the model; if absent, return "UNKNOWN".

Definition at line 452 of file GravityModel.hpp.

Referenced by main().

◆ GravityFile()

const std::string & GeographicLib::GravityModel::GravityFile ( ) const

inline

Returns: full file name used to load the gravity model.

Definition at line 457 of file GravityModel.hpp.

Referenced by main().

◆ GravityModelName()

const std::string & GeographicLib::GravityModel::GravityModelName ( ) const

inline

Returns: "name" used to load the gravity model (from the first argument of the constructor, but this may be overridden by the model file).

Definition at line 463 of file GravityModel.hpp.

Referenced by main().

◆ GravityModelDirectory()

const std::string & GeographicLib::GravityModel::GravityModelDirectory ( ) const

inline

Returns: directory used to load the gravity model.

Definition at line 468 of file GravityModel.hpp.

◆ EquatorialRadius()

Math::real GeographicLib::GravityModel::EquatorialRadius ( ) const

inline

Returns: a the equatorial radius of the ellipsoid (meters).

Definition at line 473 of file GravityModel.hpp.

References GeographicLib::NormalGravity::EquatorialRadius().

◆ MassConstant()

Math::real GeographicLib::GravityModel::MassConstant ( ) const

inline

Returns: GM the mass constant of the model (m³ s⁻²); this is the product of G the gravitational constant and M the mass of the earth (usually including the mass of the earth's atmosphere).

Definition at line 481 of file GravityModel.hpp.

◆ ReferenceMassConstant()

Math::real GeographicLib::GravityModel::ReferenceMassConstant ( ) const

inline

Returns: GM the mass constant of the ReferenceEllipsoid() (m³ s⁻²).

Definition at line 487 of file GravityModel.hpp.

References GeographicLib::NormalGravity::MassConstant().

◆ AngularVelocity()

Math::real GeographicLib::GravityModel::AngularVelocity ( ) const

inline

Returns: ω the angular velocity of the model and the ReferenceEllipsoid() (rad s⁻¹).

Definition at line 494 of file GravityModel.hpp.

References GeographicLib::NormalGravity::AngularVelocity().

◆ Flattening()

Math::real GeographicLib::GravityModel::Flattening ( ) const

inline

Returns: f the flattening of the ellipsoid.

Definition at line 500 of file GravityModel.hpp.

References GeographicLib::NormalGravity::Flattening().

◆ Degree()

int GeographicLib::GravityModel::Degree ( ) const

inline

Returns: Nmax the maximum degree of the components of the model.

Definition at line 505 of file GravityModel.hpp.

◆ Order()

int GeographicLib::GravityModel::Order ( ) const

inline

Returns: Mmax the maximum order of the components of the model.

Definition at line 510 of file GravityModel.hpp.

◆ DefaultGravityPath()

string GeographicLib::GravityModel::DefaultGravityPath ( )

static

Returns: the default path for gravity model data files.

This is the value of the environment variable GEOGRAPHICLIB_GRAVITY_PATH, if set; otherwise, it is $GEOGRAPHICLIB_DATA/gravity if the environment variable GEOGRAPHICLIB_DATA is set; otherwise, it is a compile-time default (/usr/local/share/GeographicLib/gravity on non-Windows systems and C:/ProgramData/GeographicLib/gravity on Windows systems).

Definition at line 356 of file GravityModel.cpp.

References GEOGRAPHICLIB_DATA.

Referenced by GravityModel().

◆ DefaultGravityName()

string GeographicLib::GravityModel::DefaultGravityName ( )

static

Returns: the default name for the gravity model.

This is the value of the environment variable GEOGRAPHICLIB_GRAVITY_NAME, if set; otherwise, it is "egm96". The GravityModel class does not use this function; it is just provided as a convenience for a calling program when constructing a GravityModel object.

Definition at line 369 of file GravityModel.cpp.

References GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME.

Friends And Related Function Documentation

◆ GravityCircle

friend class GravityCircle

friend

Definition at line 86 of file GravityModel.hpp.

Referenced by Circle().

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Enumeration Documentation

◆ mask

Constructor & Destructor Documentation

◆ GravityModel()

Member Function Documentation

◆ Gravity()

◆ Disturbance()

◆ GeoidHeight()

◆ SphericalAnomaly()

◆ W()

◆ V()

◆ T() [1/2]

◆ T() [2/2]

◆ U()

◆ Phi()

◆ Circle()

◆ ReferenceEllipsoid()

◆ Description()

◆ DateTime()

◆ GravityFile()

◆ GravityModelName()

◆ GravityModelDirectory()

◆ EquatorialRadius()

◆ MassConstant()

◆ ReferenceMassConstant()

◆ AngularVelocity()

◆ Flattening()

◆ Degree()

◆ Order()

◆ DefaultGravityPath()

◆ DefaultGravityName()

Friends And Related Function Documentation

◆ GravityCircle