Normal Gravity Field (pygeoid.reduction.normal)
Gravity field and geometry of the level ellipsoid.
- class pygeoid.reduction.normal.Centrifugal(omega=<Quantity 7.292115e-05 rad / s>)[source]
Centrifugal potential and its derivatives.
- Parameters:
omega (float) – Angular rotation rate of the body, in rad/s. Default value is the angular speed of Earth’s rotation 7292115e-11 rad/s
- potential(lat, radius)[source]
Return centrifugal potential.
- Parameters:
lat (Quantity) – Spherical (geocentric) latitude.
radius (Quantity) – Radius.
- Return type:
Unit(“m2 / s2”)
- r_derivative(lat, radius)[source]
Return radial derivative.
- Parameters:
lat (Quantity) – Spherical (geocentric) latitude.
radius (Quantity) – Radius.
- class pygeoid.reduction.normal.LevelEllipsoid(ellps=None, **kwargs)[source]
Class represents the gravity field of the level ellipsoid.
This class intialize Ellipsoid class from pygeoid.coordinates.ellipsoid, so all geometrical methods and parameters are available too.
- Parameters:
ellps ({'GRS80', 'WGS84', 'PZ90', 'GSK2011'}, optional) – Ellipsoid name. Default is ‘GRS80’.
- property j2
Return dynamic form factor J2.
- property gm
Return geocentric gravitational constant.
- property omega
Return angular velocity, in radians.
- property m
Auxiliary constant.
Notes
\[m = \frac{{\omega}^2 a^2 b}{GM}.\]
- property surface_potential
Return normal gravity potential on the ellipsoid.
Value of the normal gravity potential on the ellipsoid, or on the equipotential surface U(x, y, z) = U_0.
- gravitational_potential(rlat, u_ax)[source]
Return normal gravitational potential V.
Calculate normal gravitational potential from the rigorous formula.
- Parameters:
rlat (Quantity) – Reduced latitude.
u_ax (Quantity) – Polar axis of the ellipsoid passing through the point.
- Returns:
Normal gravitational potential.
- Return type:
Quantity
- gravity_potential(rlat, u_ax)[source]
Return normal gravity potential U.
Calculate normal gravity potential from the rigorous formula.
- Parameters:
rlat (Quantity) – Reduced latitude.
u_ax (Quantity) – Polar axis of the ellipsoid passing through the point.
- Returns:
Normal gravity potential.
- Return type:
Quantity
- property equatorial_normal_gravity
Return normal gravity at the equator.
- property polar_normal_gravity
Return normal gravity at the poles.
- property mean_normal_gravity
Return mean normal gravity over ellipsoid.
- property gravity_flattening
Return gravity flattening.
f* = (gamma_p - gamma_e) / gamma_e
- conventional_gravity_coeffs()[source]
Return coefficients for the conventional gravity formula.
gamma_0 = gamma_e*(1 + beta*sin(lat)**2 - beta1*sin(2*lat)**2)
- surface_normal_gravity(lat)[source]
Return normal gravity on the ellipsoid.
Calculate normal gravity value on the level ellipsoid by the rigorous formula of Somigliana.
- Parameters:
lat (Quantity) – Geodetic latitude.
- Returns:
Normal gravity on the ellipsoid.
- Return type:
Quantity
- surface_vertical_normal_gravity_gradient(lat)[source]
Return the vertical gravity gradient on the ellipsoid.
Vertical gradient of the normal gravity at the reference ellipsoid.
- Parameters:
lat (Quantity) – Geodetic latitude.
- height_correction(lat, height)[source]
Return height correction.
Second-order approximation formula is used instead of -0.3086*height.
- Parameters:
lat (Quantity) – Geodetic latitude.
height (Quantity) – Geodetic height.
- Return type:
Unit(“m / s2”)
- normal_gravity(rlat, u_ax)[source]
Return normal gravity.
Calculate normal gravity value at any arbitrary point by the rigorous closed formula.
- Parameters:
rlat (Quantity) – Reduced latitude.
u_ax (Quantity) – Polar axis of the ellipsoid passing through the point.
- Returns:
Normal gravity.
- Return type:
Quantity
- j2n(n)[source]
Return even zonal coefficients J with a degree of 2*n.
If n = 0, the function will return -1. If n = 1, the function will return J2 (dynamic form factor). If n = 2, the function will return J4. If n = 3, the function will return J6. If n = 4, the function will return J8.
- Parameters:
n (int) – Degree of the J coefficient.
- Return type:
Unit(dimensionless)
- gravitational_potential_sph(lat, radius, n_max=4)[source]
Return normal gravitational potential V.
Calculate normal gravitational potential from spherical approximation.
- Parameters:
lat (Quantity) – Spherical (geocentric) latitude.
radius (Quantity) – Radius, in metres.
n_max (int) – Maximum degree.
- Return type:
Unit(“m2 / s2”)
- gravity_potential_sph(lat, radius, n_max=4)[source]
Return normal gravitational potential V.
Calculate normal gravitational potential from spherical approximation.
- Parameters:
lat (Quantity) – Spherical (geocentric) latitude.
radius (Quantity) – Radius, in metres.
n_max (int) – Maximum degree.
- Return type:
Unit(“m2 / s2”)
- pygeoid.reduction.normal.surface_normal_gravity_clairaut(lat, model=None)[source]
Return normal gravity from the first Clairaut formula.
- Parameters:
lat (Quantity) – Geodetic latitude.
model ({'helmert', 'helmert_14mGal', '1930', '1930_14mGal', '1967', '1980'}) – Which gravity formula will be used.
- Return type:
Unit(“m / s2”)