GeographicLib::GravityCircle Class Reference

Gravity on a circle of latitude. More...

#include <GeographicLib/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	EquatorialRadius () const
Math::real	Flattening () const
Math::real	Latitude () const
Math::real	Height () const
unsigned	Capabilities () const
bool	Capabilities (unsigned testcaps) const

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 Geoid heights on a multi-processor system 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
// 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>
#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.

Constructor & Destructor Documentation

GravityCircle()

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 83 of file GravityCircle.hpp.

Member Function Documentation

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 51 of file GravityCircle.cpp.

Referenced by main().

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 61 of file GravityCircle.cpp.

Referenced by main().

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 Details of the geoid height and anomaly calculations.

Definition at line 71 of file GravityCircle.cpp.

Referenced by main().

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 Details of the geoid height and anomaly calculations.

Definition at line 81 of file GravityCircle.cpp.

Referenced by main().

W()

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 166 of file GravityCircle.hpp.

References GeographicLib::Math::sincosd().

V()

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 186 of file GravityCircle.hpp.

References GeographicLib::Math::sincosd().

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 206 of file GravityCircle.hpp.

References GeographicLib::Math::sincosd().

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 220 of file GravityCircle.hpp.

References GeographicLib::Math::sincosd().

Init()

bool GeographicLib::GravityCircle::Init ( ) const

inline

Returns

true if the object has been initialized.

Definition at line 234 of file GravityCircle.hpp.

EquatorialRadius()

Math::real GeographicLib::GravityCircle::EquatorialRadius ( ) 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 241 of file GravityCircle.hpp.

References GeographicLib::Math::NaN().

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 248 of file GravityCircle.hpp.

References GeographicLib::Math::NaN().

Latitude()

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

inline

Returns

the latitude of the circle (degrees).

Definition at line 254 of file GravityCircle.hpp.

References GeographicLib::Math::NaN().

Height()

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

inline

Returns

the height of the circle (meters).

Definition at line 260 of file GravityCircle.hpp.

References GeographicLib::Math::NaN().

Capabilities() [1/2]

unsigned GeographicLib::GravityCircle::Capabilities ( ) const

inline

Returns

caps the computational capabilities that this object was constructed with.

Definition at line 267 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 273 of file GravityCircle.hpp.

Friends And Related Function Documentation

GravityModel

friend class GravityModel

friend

Definition at line 69 of file GravityCircle.hpp.

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

• GravityCircle.hpp
• GravityCircle.cpp