GeographicLib  1.48
GeographicLib::GravityModel Class Reference

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

#include <GeographicLib/GravityModel.hpp>

## Public Types

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="")

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 NormalGravityReferenceEllipsoid () 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 MassConstant () const

Math::real ReferenceMassConstant () const

Math::real AngularVelocity () const

Math::real Flattening () 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 atomsphere 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 = WU = VV0 = anomalous or disturbing potential;
• g = ∇W = γ + δ;
• f = ∇Φ;
• Γ = ∇V0;
• γ = ∇U;
• δ = ∇T = gravity disturbance vector = gPγP;
• δg = gravity disturbance = gP − γP;
• Δg = gravity anomaly vector = gPγQ; here the line PQ is perpendicular to ellipsoid and the potential at P equals the normal potential at Q;
• Δg = gravity anomaly = gP − γQ;
• (ξ, η) deflection of the vertical, the difference in directions of gP and γQ, 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
#include <iostream>
#include <exception>
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

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 121 of file GravityModel.hpp.

## ◆ GravityModel()

 GeographicLib::GravityModel::GravityModel ( const std::string & name, const std::string & path = "" )
explicit

Construct a gravity model.

Parameters
 [in] name the name of the model. [in] path (optional) directory for data file.
Exceptions
 GeographicErr if the data file cannot be found, is unreadable, or is corrupt. 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").

Definition at line 37 of file GravityModel.cpp.

## ◆ 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 290 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 298 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 276 of file GravityModel.cpp.

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 249 of file GravityModel.cpp.

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 240 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 228 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 326 of file GravityModel.hpp.

Referenced by GeoidHeight(), GravityModel(), 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 339 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 363 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 381 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 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 308 of file GravityModel.cpp.

Referenced by main().

## ◆ ReferenceEllipsoid()

 const NormalGravity& GeographicLib::GravityModel::ReferenceEllipsoid ( ) const
inline
Returns
the NormalGravity object for the reference ellipsoid.

Definition at line 430 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 436 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 441 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 446 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 452 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 457 of file GravityModel.hpp.

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

Definition at line 462 of file GravityModel.hpp.

## ◆ 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 470 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 476 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 483 of file GravityModel.hpp.

## ◆ Flattening()

 Math::real GeographicLib::GravityModel::Flattening ( ) const
inline
Returns
f the flattening of the ellipsoid.

Definition at line 489 of file GravityModel.hpp.

References GeographicLib::NormalGravity::Flattening().

## ◆ DefaultGravityPath()

 std::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 342 of file GravityModel.cpp.

References GEOGRAPHICLIB_DATA.

Referenced by GravityModel(), and main().

## ◆ DefaultGravityName()

 std::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 355 of file GravityModel.cpp.

References GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME.

Referenced by main().

## ◆ 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: