GeographicLib::GravityCircle Class Reference

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 ) 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.

T() [2/2]

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.

V() [1/2]

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.

V() [2/2]

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.

W() [1/2]

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.

W() [2/2]

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.

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 56 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 57 of file GravityCircle.hpp.

_cphi

real GeographicLib::GravityCircle::_cphi

private

Definition at line 56 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 56 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 57 of file GravityCircle.hpp.

_gamma

real GeographicLib::GravityCircle::_gamma

private

Definition at line 57 of file GravityCircle.hpp.

_gamma0

real GeographicLib::GravityCircle::_gamma0

private

Definition at line 57 of file GravityCircle.hpp.

_GMmodel

real GeographicLib::GravityCircle::_GMmodel

private

Definition at line 56 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 56 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.

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

• GravityCircle.hpp
• src/GravityCircle.cpp