Gravity on a circle of latitude. More...

#include <GravityCircle.hpp>

Public Member Functions
	GravityCircle ()

Compute the gravitational field
Math::real	Gravity (real lon, real &gx, real &gy, real &gz) const

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

Math::real	GeoidHeight (real lon) const

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

Math::real	W (real lon, real &gX, real &gY, real &gZ) const

Math::real	V (real lon, real &GX, real &GY, real &GZ) const

Math::real	T (real lon, real &deltaX, real &deltaY, real &deltaZ) const

Math::real	T (real lon) const

Inspector functions
bool	Init () const

Math::real	MajorRadius () const

Math::real	Flattening () const

Math::real	Latitude () const

Math::real	Height () const

unsigned	Capabilities () const

bool	Capabilities (unsigned testcaps) const

Private Types
enum	mask { NONE = GravityModel::NONE, GRAVITY = GravityModel::GRAVITY, DISTURBANCE = GravityModel::DISTURBANCE, DISTURBING_POTENTIAL = GravityModel::DISTURBING_POTENTIAL, GEOID_HEIGHT = GravityModel::GEOID_HEIGHT, SPHERICAL_ANOMALY = GravityModel::SPHERICAL_ANOMALY, ALL = GravityModel::ALL }

typedef Math::real	real

Private Member Functions
	GravityCircle (mask caps, real a, real f, real lat, real h, real Z, real P, real cphi, real sphi, real amodel, real GMmodel, real dzonal0, real corrmult, real gamma0, real gamma, real frot, const CircularEngine &gravitational, const CircularEngine &disturbing, const CircularEngine &correction)

Math::real	InternalT (real slam, real clam, real &deltaX, real &deltaY, real &deltaZ, bool gradp, bool correct) const

Math::real	V (real slam, real clam, real &gX, real &gY, real &gZ) const

Math::real	W (real slam, real clam, real &gX, real &gY, real &gZ) const

Private Attributes
real	_a

real	_amodel

unsigned	_caps

CircularEngine	_correction

real	_corrmult

real	_cphi

real	_cpsi

CircularEngine	_disturbing

real	_dzonal0

real	_f

real	_frot

real	_gamma

real	_gamma0

real	_GMmodel

CircularEngine	_gravitational

real	_h

real	_invR

real	_lat

real	_Px

real	_sphi

real	_spsi

real	_Z

Friends
class	GravityModel

Detailed Description

Gravity on a circle of latitude.

Evaluate the earth's gravity field on a circle of constant height and latitude. This uses a CircularEngine to pre-evaluate the inner sum of the spherical harmonic sum, allowing the values of the field at several different longitudes to be evaluated rapidly.

Use GravityModel::Circle to create a GravityCircle object. (The constructor for this class is private.)

See gravityparallel for an example of using GravityCircle (together with OpenMP) to speed up the computation of geoid heights.

Example of use:

// Example of using the GeographicLib::GravityCircle class
#include <iostream>
#include <exception>
#include <GeographicLib/GravityModel.hpp>
#include <GeographicLib/GravityCircle.hpp>
using namespace std;
using namespace GeographicLib;
int main() {
  try {
    GravityModel grav("egm96");
    double lat = 27.99, lon0 = 86.93, h = 8820; // Mt Everest
    {
      // Slow method of evaluating the values at several points on a circle of
      // latitude.
      for (int i = -5; i <= 5; ++i) {
        double lon = lon0 + i * 0.2;
        double gx, gy, gz;
        grav.Gravity(lat, lon, h, gx, gy, gz);
        cout << lon << " " << gx << " " << gy << " " << gz << "\n";
      }
    }
    {
      // Fast method of evaluating the values at several points on a circle of
      // latitude using GravityCircle.
      GravityCircle circ = grav.Circle(lat, h);
      for (int i = -5; i <= 5; ++i) {
        double lon = lon0 + i * 0.2;
        double gx, gy, gz;
        circ.Gravity(lon, gx, gy, gz);
        cout << lon << " " << 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 41 of file GravityCircle.hpp.

Member Typedef Documentation

◆ real

typedef Math::real GeographicLib::GravityCircle::real

private

Definition at line 43 of file GravityCircle.hpp.

Member Enumeration Documentation

◆ mask

enum GeographicLib::GravityCircle::mask

private

Enumerator
NONE
GRAVITY
DISTURBANCE
DISTURBING_POTENTIAL
GEOID_HEIGHT
SPHERICAL_ANOMALY
ALL

Definition at line 44 of file GravityCircle.hpp.

Constructor & Destructor Documentation

◆ GravityCircle() [1/2]

GeographicLib::GravityCircle::GravityCircle	(	mask	caps,
		real	a,
		real	f,
		real	lat,
		real	h,
		real	Z,
		real	P,
		real	cphi,
		real	sphi,
		real	amodel,
		real	GMmodel,
		real	dzonal0,
		real	corrmult,
		real	gamma0,
		real	gamma,
		real	frot,
		const CircularEngine &	gravitational,
		const CircularEngine &	disturbing,
		const CircularEngine &	correction
	)

inlineprivate

Definition at line 60 of file GravityCircle.hpp.

◆ GravityCircle() [2/2]

GeographicLib::GravityCircle::GravityCircle ( )

inline

A default constructor for the normal gravity. This sets up an uninitialized object which can be later replaced by the GravityModel::Circle.

Definition at line 105 of file GravityCircle.hpp.

Member Function Documentation

◆ Capabilities() [1/2]

unsigned GeographicLib::GravityCircle::Capabilities ( ) const

inline

Returns: caps the computational capabilities that this object was constructed with.

Definition at line 289 of file GravityCircle.hpp.

◆ Capabilities() [2/2]

bool GeographicLib::GravityCircle::Capabilities ( unsigned testcaps ) const

inline

Parameters

[in] testcaps a set of bitor'ed GravityModel::mask values.

Returns: true if the GravityCircle object has all these capabilities.

Definition at line 295 of file GravityCircle.hpp.

◆ Disturbance()

Math::real GeographicLib::GravityCircle::Disturbance	(	real	lon,
		real &	deltax,
		real &	deltay,
		real &	deltaz
	)		const

Evaluate the gravity disturbance vector.

Parameters

[in]	lon	the geographic longitude (degrees).
[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 29 of file src/GravityCircle.cpp.

◆ Flattening()

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

inline

Returns: f the flattening of the ellipsoid. This is the value inherited from the GravityModel object used in the constructor.

Definition at line 270 of file GravityCircle.hpp.

◆ GeoidHeight()

Math::real GeographicLib::GravityCircle::GeoidHeight ( real lon ) const

Evaluate the geoid height.

Parameters

[in] lon the geographic longitude (degrees).

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

Some approximations are made in computing the geoid height so that the results of the NGA codes are reproduced accurately. Details are given in gravitygeoid.

Definition at line 39 of file src/GravityCircle.cpp.

◆ Gravity()

Math::real GeographicLib::GravityCircle::Gravity	(	real	lon,
		real &	gx,
		real &	gy,
		real &	gz
	)		const

Evaluate the gravity.

Parameters

[in]	lon	the geographic longitude (degrees).
[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 19 of file src/GravityCircle.cpp.

◆ Height()

Math::real GeographicLib::GravityCircle::Height ( ) const

inline

Returns: the height of the circle (meters).

Definition at line 282 of file GravityCircle.hpp.

◆ Init()

bool GeographicLib::GravityCircle::Init ( ) const

inline

Returns: true if the object has been initialized.

Definition at line 256 of file GravityCircle.hpp.

◆ InternalT()

Math::real GeographicLib::GravityCircle::InternalT	(	real	slam,
		real	clam,
		real &	deltaX,
		real &	deltaY,
		real &	deltaZ,
		bool	gradp,
		bool	correct
	)		const

private

Definition at line 94 of file src/GravityCircle.cpp.

◆ Latitude()

Math::real GeographicLib::GravityCircle::Latitude ( ) const

inline

Returns: the latitude of the circle (degrees).

Definition at line 276 of file GravityCircle.hpp.

◆ MajorRadius()

Math::real GeographicLib::GravityCircle::MajorRadius ( ) const

inline

Returns: a the equatorial radius of the ellipsoid (meters). This is the value inherited from the GravityModel object used in the constructor.

Definition at line 263 of file GravityCircle.hpp.

◆ SphericalAnomaly()

void GeographicLib::GravityCircle::SphericalAnomaly	(	real	lon,
		real &	Dg01,
		real &	xi,
		real &	eta
	)		const

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

Parameters

[in]	lon	the geographic longitude (degrees).
[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 gravitygeoid.

Definition at line 49 of file src/GravityCircle.cpp.

◆ T() [1/2]

Math::real GeographicLib::GravityCircle::T	(	real	lon,
		real &	deltaX,
		real &	deltaY,
		real &	deltaZ
	)		const

inline

Evaluate the components of the gravity disturbance in geocentric coordinates.

Parameters

[in]	lon	the geographic longitude (degrees).
[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 228 of file GravityCircle.hpp.

◆ T() [2/2]

Math::real GeographicLib::GravityCircle::T ( real lon ) const

inline

Evaluate disturbing potential in geocentric coordinates.

Parameters

[in] lon the geographic longitude (degrees).

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

Definition at line 242 of file GravityCircle.hpp.

◆ V() [1/2]

Math::real GeographicLib::GravityCircle::V	(	real	slam,
		real	clam,
		real &	gX,
		real &	gY,
		real &	gZ
	)		const

private

Definition at line 78 of file src/GravityCircle.cpp.

◆ V() [2/2]

Math::real GeographicLib::GravityCircle::V	(	real	lon,
		real &	GX,
		real &	GY,
		real &	GZ
	)		const

inline

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

Parameters

[in]	lon	the geographic longitude (degrees).
[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 208 of file GravityCircle.hpp.

◆ W() [1/2]

Math::real GeographicLib::GravityCircle::W	(	real	slam,
		real	clam,
		real &	gX,
		real &	gY,
		real &	gZ
	)		const

private

Definition at line 70 of file src/GravityCircle.cpp.

◆ W() [2/2]

Math::real GeographicLib::GravityCircle::W	(	real	lon,
		real &	gX,
		real &	gY,
		real &	gZ
	)		const

inline

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

Parameters

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

Definition at line 188 of file GravityCircle.hpp.

Friends And Related Function Documentation

◆ GravityModel

friend class GravityModel

friend

Definition at line 91 of file GravityCircle.hpp.

Member Data Documentation

◆ _a

real GeographicLib::GravityCircle::_a

private

Definition at line 55 of file GravityCircle.hpp.

◆ _amodel

real GeographicLib::GravityCircle::_amodel

private

Definition at line 55 of file GravityCircle.hpp.

◆ _caps

unsigned GeographicLib::GravityCircle::_caps

private

Definition at line 54 of file GravityCircle.hpp.

◆ _correction

CircularEngine GeographicLib::GravityCircle::_correction

private

Definition at line 58 of file GravityCircle.hpp.

◆ _corrmult

real GeographicLib::GravityCircle::_corrmult

private

Definition at line 55 of file GravityCircle.hpp.

◆ _cphi

real GeographicLib::GravityCircle::_cphi

private

Definition at line 55 of file GravityCircle.hpp.

◆ _cpsi

real GeographicLib::GravityCircle::_cpsi

private

Definition at line 55 of file GravityCircle.hpp.

◆ _disturbing

CircularEngine GeographicLib::GravityCircle::_disturbing

private

Definition at line 58 of file GravityCircle.hpp.

◆ _dzonal0

real GeographicLib::GravityCircle::_dzonal0

private

Definition at line 55 of file GravityCircle.hpp.

◆ _f

real GeographicLib::GravityCircle::_f

private

Definition at line 55 of file GravityCircle.hpp.

◆ _frot

real GeographicLib::GravityCircle::_frot

private

Definition at line 55 of file GravityCircle.hpp.

◆ _gamma

real GeographicLib::GravityCircle::_gamma

private

Definition at line 55 of file GravityCircle.hpp.

◆ _gamma0

real GeographicLib::GravityCircle::_gamma0

private

Definition at line 55 of file GravityCircle.hpp.

◆ _GMmodel

real GeographicLib::GravityCircle::_GMmodel

private

Definition at line 55 of file GravityCircle.hpp.

◆ _gravitational

CircularEngine GeographicLib::GravityCircle::_gravitational

private

Definition at line 58 of file GravityCircle.hpp.

◆ _h

real GeographicLib::GravityCircle::_h

private

Definition at line 55 of file GravityCircle.hpp.

◆ _invR

real GeographicLib::GravityCircle::_invR

private

Definition at line 55 of file GravityCircle.hpp.

◆ _lat

real GeographicLib::GravityCircle::_lat

private

Definition at line 55 of file GravityCircle.hpp.

◆ _Px

real GeographicLib::GravityCircle::_Px

private

Definition at line 55 of file GravityCircle.hpp.

◆ _sphi

real GeographicLib::GravityCircle::_sphi

private

Definition at line 55 of file GravityCircle.hpp.

◆ _spsi

real GeographicLib::GravityCircle::_spsi

private

Definition at line 55 of file GravityCircle.hpp.

◆ _Z

real GeographicLib::GravityCircle::_Z

private

Definition at line 55 of file GravityCircle.hpp.

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

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ real

Member Enumeration Documentation

◆ mask

Constructor & Destructor Documentation

◆ GravityCircle() [1/2]

◆ GravityCircle() [2/2]

Member Function Documentation

◆ Capabilities() [1/2]

◆ Capabilities() [2/2]

◆ Disturbance()

◆ Flattening()

◆ GeoidHeight()

◆ Gravity()

◆ Height()

◆ Init()

◆ InternalT()

◆ Latitude()

◆ MajorRadius()

◆ SphericalAnomaly()

◆ T() [1/2]

◆ T() [2/2]

◆ V() [1/2]

◆ V() [2/2]

◆ W() [1/2]

◆ W() [2/2]

Friends And Related Function Documentation

◆ GravityModel

Member Data Documentation

◆ _a

◆ _amodel

◆ _caps

◆ _correction

◆ _corrmult

◆ _cphi

◆ _cpsi

◆ _disturbing

◆ _dzonal0

◆ _f

◆ _frot

◆ _gamma

◆ _gamma0

◆ _GMmodel

◆ _gravitational

◆ _h

◆ _invR

◆ _lat

◆ _Px

◆ _sphi

◆ _spsi

◆ _Z