def test_surface_normal_gravity():
ell = LevelEllipsoid('GRS80')
np.testing.assert_almost_equal(
ell.surface_normal_gravity(0. * u.deg).value,
ell.equatorial_normal_gravity.value, decimal=9)
np.testing.assert_almost_equal(
ell.surface_normal_gravity(90. * u.deg).value,
ell.polar_normal_gravity.value, decimal=9)
# geodetic latitude
lat = np.arange(-90, 90, 0.1, dtype=float) * u.deg
rlat, _, u_ax = transform.geodetic_to_ellipsoidal(lat=lat,
lon=0.0 * u.deg,
height=0.0 * u.m, ell=ell)
normal_gravity_somigliana = ell.surface_normal_gravity(lat)
normal_gravity_ell = ell.normal_gravity(rlat, u_ax)
np.testing.assert_almost_equal(
normal_gravity_somigliana.value,
normal_gravity_ell.value,
decimal=9)
# approximate formula (Clairaut)
beta, beta1 = ell.conventional_gravity_coeffs()
ge = ell.equatorial_normal_gravity
latrad = np.radians(lat)
normal_gravity_approx = ge*(1 + beta*np.sin(latrad)**2 -
beta1*np.sin(2*latrad)**2)
np.testing.assert_almost_equal(
normal_gravity_somigliana.value,
normal_gravity_approx.value,
decimal=6)
np.testing.assert_almost_equal(
surface_normal_gravity_clairaut(lat, '1980').to('mGal').value,
normal_gravity_approx.to('mGal').value,
decimal=1)
def test_normal_gravity():
ell = LevelEllipsoid('GRS80')
# geodetic latitude
lat = np.arange(-90, 90, 0.5, dtype=np.float64)
height = np.arange(1, 10e3, 100, dtype=np.float64)
latv, heightv = np.meshgrid(lat, height, indexing='xy')
height_corr = ell.height_correction(latv, heightv)
normal_gravity_somigliana = ell.surface_normal_gravity(latv)
normal_gravity_1 = normal_gravity_somigliana + height_corr
rlat, _, u = transform.geodetic_to_ellipsoidal(lat=latv,
lon=0.0, height=heightv, ell=ell)
normal_gravity_2 = ell.normal_gravity(rlat, u)
np.testing.assert_almost_equal(
normal_gravity_1,
normal_gravity_2,
decimal=6)
def test_against_GRS80():
# Moritz, H., 1980. Geodetic reference system 1980.
# Bulletin géodésique, 54(3), pp.395-405.
ell = LevelEllipsoid('GRS80')
# geometric constants
np.testing.assert_equal(ell.a, 6378137.0)
np.testing.assert_almost_equal(ell.b, 6356752.3141, decimal=4)
np.testing.assert_almost_equal(ell.linear_eccentricity,
521854.0097, decimal=4)
np.testing.assert_almost_equal(ell.polar_curvature_radius,
6399593.6259, decimal=4)
np.testing.assert_almost_equal(ell.eccentricity_squared,
0.00669438002290, decimal=14)
np.testing.assert_almost_equal(ell.second_eccentricity_squared,
0.00673949677548, decimal=14)
np.testing.assert_almost_equal(ell.flattening,
0.00335281068118, decimal=14)
np.testing.assert_almost_equal(ell.reciprocal_flattening,
298.257222101, decimal=9)
np.testing.assert_almost_equal(ell.quadrant_distance,
10001965.7293, decimal=4)
np.testing.assert_almost_equal(ell.surface_area * 1e-014,
5.10065622, decimal=8)
np.testing.assert_almost_equal(ell.volume * 1e-021,
1.08320732, decimal=8)
# mean radius
kind = 'arithmetic'
np.testing.assert_almost_equal(
ell.mean_radius(kind), 6371008.7714, decimal=4)
kind = 'same_area'
np.testing.assert_almost_equal(ell.mean_radius(kind),
6371007.1810, decimal=4)
kind = 'same_volume'
np.testing.assert_almost_equal(ell.mean_radius(kind),
6371000.7900, decimal=4)
# physical constants
np.testing.assert_almost_equal(ell.surface_potential,
62636860.850, decimal=3)
np.testing.assert_almost_equal(ell.equatorial_normal_gravity,
9.7803267715, decimal=10)
np.testing.assert_almost_equal(ell.polar_normal_gravity,
9.8321863685, decimal=10)
np.testing.assert_almost_equal(ell.gravity_flattening,
0.005302440112, decimal=12)
np.testing.assert_almost_equal(ell._k,
0.001931851353, decimal=12)
np.testing.assert_almost_equal(ell.m,
0.00344978600308, decimal=14)
np.testing.assert_almost_equal(ell.j2n(n=2),
-0.00000237091222, decimal=14)
np.testing.assert_almost_equal(ell.j2n(n=3),
0.00000000608347, decimal=14)
np.testing.assert_almost_equal(ell.j2n(n=4),
-0.00000000001427, decimal=14)
np.testing.assert_almost_equal(ell.surface_normal_gravity(45.),
9.806199203, decimal=9)
np.testing.assert_almost_equal(ell.conventional_gravity_coeffs()[-1],
0.0000058, decimal=7)
# other
np.testing.assert_almost_equal(ell.mean_normal_gravity,
9.797644656, decimal=9)
np.testing.assert_almost_equal(
ell.surface_normal_gravity(45.),
9.806199203, decimal=9)