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Tesseroids 1.0: User Manual and API Documentation |
Functions that calculate the gravitational potential and its first and second derivatives for the sphere in spherical coordinates. More...
#include "utils.h"
Go to the source code of this file.
Functions | |
double | sphere_pot (SPHERE sphere, double lonp, double latp, double rp) |
Calculates potential caused by a sphere. | |
double | sphere_gx (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gx caused by a sphere (Grombein et al., 2010). | |
double | sphere_gy (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gy caused by a sphere (Grombein et al., 2010). | |
double | sphere_gz (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gz caused by a sphere (Grombein et al., 2010). | |
double | sphere_gxx (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gxx caused by a sphere (Grombein et al., 2010). | |
double | sphere_gxy (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gxy caused by a sphere (Grombein et al., 2010). | |
double | sphere_gxz (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gxz caused by a sphere (Grombein et al., 2010). | |
double | sphere_gyy (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gyy caused by a sphere (Grombein et al., 2010). | |
double | sphere_gyz (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gyz caused by a sphere (Grombein et al., 2010). | |
double | sphere_gzz (SPHERE sphere, double lonp, double latp, double rp) |
Calculates gzz caused by a sphere (Grombein et al., 2010). |
Functions that calculate the gravitational potential and its first and second derivatives for the sphere in spherical coordinates.
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out. So it would be normal for a sphere of positive density to have negative gz.
Used the generic formula for gravity gradient computation (Grombein et al., 2010):
where M is the mass of the sphere, the subscripts 1, 2, and 3 should be interpreted as the x, y, and z axis and
is latitude,
is longitude,
is radius. The subscript
is for the center of the sphere and
for the computation point.
References
double sphere_gx | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gx caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point should be in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in mGal!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gxx | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gxx caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in Eotvos!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gxy | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gxy caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in Eotvos!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gxz | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gxz caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in Eotvos!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gy | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gy caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point should be in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in mGal!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gyy | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gyy caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in Eotvos!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gyz | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gyz caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in Eotvos!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gz | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gz caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point should be in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in mGal!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_gzz | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates gzz caused by a sphere (Grombein et al., 2010).
The position of the sphere and computation point are in spherical coordinates.
The derivatives of the potential are made with respect to the local coordinate system x->North, y->East, z->out
Input values in SI units and degrees and returns values in Eotvos!
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |
double sphere_pot | ( | SPHERE | sphere, | |
double | lonp, | |||
double | latp, | |||
double | rp | |||
) |
Calculates potential caused by a sphere.
The position of the sphere and computation point should be in spherical coordinates.
Input and output values in SI units and degrees
sphere | data structure describing the sphere | |
lonp | longitude of the computation point P | |
latp | latitude of the computation point P | |
rp | radial coordinate of the computation point P |