GeographicLib: GeographicLib::GravityCircle Class Reference

GeographicLib 2.6

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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;
}
}
main
int main(int argc, const char *const argv[])
Definition Cart3Convert.cpp:52
GravityCircle.hpp
Header for GeographicLib::GravityCircle class.
GravityModel.hpp
Header for GeographicLib::GravityModel class.
GeographicLib::GravityCircle
Gravity on a circle of latitude.
Definition GravityCircle.hpp:41
GeographicLib::GravityCircle::Gravity
Math::real Gravity(real lon, real &gx, real &gy, real &gz) const
Definition GravityCircle.cpp:51
GeographicLib::GravityCircle::GravityModel
friend class GravityModel
Definition GravityCircle.hpp:69
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806

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.

References Gravity(), and GeographicLib::Math::sincosd().

Referenced by Gravity(), and 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.

References Disturbance(), and GeographicLib::Math::sincosd().

Referenced by Disturbance(), and 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.

References GeoidHeight(), GeographicLib::Math::NaN(), GeographicLib::Math::sincosd(), and T().

Referenced by GeoidHeight(), and 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.

References GeographicLib::Math::degree(), GeographicLib::Math::NaN(), GeographicLib::Math::sincosd(), SphericalAnomaly(), and T().

Referenced by main(), and SphericalAnomaly().

## ◆ 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().

Referenced by GeoidHeight(), and SphericalAnomaly().

## ◆ 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.

Referenced by EquatorialRadius(), Flattening(), Height(), and Latitude().

## ◆ 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 Init(), and 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 Init(), and 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 Init(), and 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 Init(), and 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 Symbol Documentation

## ◆ GravityModel

friend class GravityModel
| friend

Definition at line 69 of file GravityCircle.hpp.

References GravityModel.

Referenced by GravityModel.

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

- GravityCircle.hpp
- GravityCircle.cpp