def test_latitude_dependend_values():
# From
# Deakin, R.E. and Hunter, M.N., 2010. Geometric geodesy part A. Lecture
# Notes, School of Mathematical & Geospatial Sciences, RMIT University,
# Melbourne, Australia.
# pp. 87 - 88
ell = Ellipsoid('GRS80')
lat = -(37 + 48 / 60 + 33.1234 / 3600) * u.deg
np.testing.assert_almost_equal(ell._w(lat).value, 0.998741298, decimal=9)
np.testing.assert_almost_equal(ell._v(lat).value, 1.002101154, decimal=9)
np.testing.assert_almost_equal(ell.meridian_curvature_radius(lat).value,
6359422.962,
decimal=3)
np.testing.assert_almost_equal(
ell.prime_vertical_curvature_radius(lat).value, 6386175.289, decimal=3)
np.testing.assert_almost_equal(ell.mean_curvature(lat).value,
1 / 6372785.088,
decimal=16)
np.testing.assert_almost_equal(ell.meridian_arc_distance(0.0 * u.deg,
lat).value,
4186320.340,
decimal=3)
def gravity_ell(self,
lat: u.deg,
height: u.m,
ell: Ellipsoid,
elastic: bool = True) -> u.m / u.s**2:
"""Return permanent tidal gravity variation along the ellipsoidal normal.
Parameters
----------
lat : ~astropy.units.Quantity
Geodetic latitude.
height : ~astropy.units.Quantity
Geodetic height.
ell : ~pygeoid.coordinates.ellipsoid.Ellipsoid
Reference ellipsoid to which geodetic coordinates are referenced to.
elastic : bool, optional
If True then the Earth is elastic (deformable)
and gravity change is multiplied by the gravimetric factor
specified in the class instance.
Returns
-------
delta_g : ~astropy.units.Quantity
Permanent tidal potential gravity variation.
"""
pvcr = ell.prime_vertical_curvature_radius(lat.radian) * u.m
delta_g = 2 / 3 * self.coeff / self.r0**2 * (
(pvcr *
(3 - 2 * ell.e2) + 3 * height) * np.sin(lat)**2 - (pvcr + height))
if elastic:
delta_g *= self.gravimetric_factor
return -delta_g