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Update tidal model documentation structure
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@fbriol
fbriol committed Jul 2, 2024
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Showing 1 changed file with 158 additions and 90 deletions.
248 changes: 158 additions & 90 deletions examples/ex_astronomic_constants.py
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Expand Up @@ -109,20 +109,27 @@ def astronomic_constants() -> AstronomicConstants:
"""Astronomic constants."""
# Mass (of sun/mass) of earthy (S/E)
SE = 332946.0487

# Mass of moon/mass of earth (M/E)
ME = 0.0123000371

# Solar parallex
c1 = dms_to_deg(0, 0, 8.794_143)

# Lunar equatorial parallex
c = dms_to_deg(0, 57, 2.70)
mean_earth_radius = 6_371_008.771415059
earth_equatorial_radius = 6_378_137.0

# Mean solar parallax in respect to mean radius
ac1 = (mean_earth_radius / earth_equatorial_radius) * c1

# Mean lunar parallax in respect to mean radius
ac = (mean_earth_radius / earth_equatorial_radius) * c

# Solar coefficient U1 (SE) * ac1^3
u1: float = SE * ac1**3

# Basic factor U (ME) * ac^3
u: float = ME * ac**3

Expand All @@ -136,127 +143,189 @@ def astronomic_constants() -> AstronomicConstants:


# %%
# Schureman's values
# ------------------
const = schureman_values()
const
print(const)

# %%
# Page 25, formulae #73, Page 24, formulae #65
# Formulae 73, 65
# ---------------
# `Page 24, 25`
#
# * :math:`\{2/3 - sin^2(\omega)\}\{1 - 3/2 \times sin(i)\} = 0.5021`
# * :math:`f(Mm) = \{2/3 - sin^2(I)\} / 0.5021`

# %%
# .. math::
#
# \{2/3 - sin^2(\omega)\}\{1 - 3/2 \times sin(i)\} = 0.5021
#
# .. math::
#
# f(Mm) = \{2/3 - sin^2(I)\} / 0.5021
a65 = (2 / 3 - math.sin(const.w)**2) * (1 - 3 / 2 * math.sin(const.i)**2)
print(f'{a65:.4f}')

# %%
# Page 25, formulae #74, Page 24, formulae #66
# Formulae 74, 66
# ---------------
# `Page 24, 25`
#
# * :math:`sin^2(\omega) \times \cos^4(\frac{1}{2}i) = 0.1528`
# * :math:`f(Mf) = sin^2(I) / 0.1528`

# %%
# .. math::
#
# sin^2(\omega) \times \cos^4(\frac{1}{2}i) = 0.1528
#
# .. math::
#
# f(Mf) = sin^2(I) / 0.1528
a66 = math.sin(const.w)**2 * math.cos(0.5 * const.i)**4
print(f'a66 = {a66:.4f}')

# %%
# Page 25, formulae #75, Page 25, formulae #67
# Formulae 75, 67
# ---------------
# `Page 25`
#
# * :math:`sin(\omega)cos^2(\frac{1}{2}\omega)cos^4(\frac{1}{2}i) = 0.3800`
# * :math:`f(O_1) = sin(I) \times cos^2(\frac{1}{2}I) / 0.3800`

# %%
# .. math::
#
# sin(\omega)cos^2(\frac{1}{2}\omega)cos^4(\frac{1}{2}i) = 0.3800
#
# .. math::
#
# f(O_1) = sin(I) \times cos^2(\frac{1}{2}I) / 0.3800
a67 = math.sin(const.w) * math.cos(0.5 * const.w)**2 * math.cos(
0.5 * const.i)**4
print(f'a67 = {a67:.4f}')

# %%
# Page 25, formulae #76, Page 25, formulae #68
# Formulae 76, 68
# ---------------
# `Page 25`
#
# * :math:`sin(2\omega) \times \{1 - 3/2 \times sin^2(i)\} = 0.7214``
# * :math:`f(J_1) = sin(2I) / 0.7214``

# %%
# .. math::
#
# sin(2\omega) \times \{1 - 3/2 \times sin^2(i)\} = 0.7214
#
# .. math::
#
# f(J_1) = sin(2I) / 0.7214
a68 = math.sin(2 * const.w) * (1 - 3 / 2 * math.sin(const.i)**2)
print(f'a68 = {a68:.4f}')

# %%
# Page 25, formulae #77, Page 25, formulae #69
# Formulae 77, 69
# ---------------
# `Page 25`
#
# * .. math::
# .. math::
#
# sin(\omega) \times sin^2(\frac{1}{2}\omega)
# \times cos^4(\frac{1}{2}i) = 0.0164``
#
# * :math:`f(OO_1) = sin(I) \times sin^2(\frac{1}{2}I) / 0.0164``

# %%
# .. math::
#
# f(OO_1) = sin(I) \times sin^2(\frac{1}{2}I) / 0.0164
a69 = math.sin(const.w) * math.sin(0.5 * const.w)**2 * math.cos(
0.5 * const.i)**4
print(f'a69 = {a69:.4f}')

# %%
# Page 25, formulae #78, Page 25, formulae #70
# Formulae 78, 70
# ---------------
# `Page 25`
#
# * :math:`cos^4(\frac{1}{2}\omega) \times cos^4(\frac{1}{2}i) = 0.9154`
# * :math:`f(M_2) = sin^4(\frac{1}{2}I) / 0.9154`

# %%
# .. math::
#
# cos^4(\frac{1}{2}\omega) \times cos^4(\frac{1}{2}i) = 0.9154
#
# .. math::
#
# f(M_2) = sin^4(\frac{1}{2}I) / 0.9154
a70 = math.cos(0.5 * const.w)**4 * math.cos(0.5 * const.i)**4
print(f'a70 = {a70:.4f}')

# %%
# Page 25, formulae #79, Page 25, formulae #71
# Formulae 79, 71
# ---------------
# `Page 25`
#
# * :math:`sin^2(\omega) \times (1 -3/2 \times sin^2(i))`
# * :math:`f(79) = sin^2I / 0.1565`

# %%
# .. math::
#
# sin^2(\omega) \times (1 -3/2 \times sin^2(i))
#
# .. math::
#
# f(79) = sin^2I / 0.1565
a71 = math.sin(const.w)**2 * (1 - 3 / 2 * math.sin(const.i)**2)
print(f'a71 = {a71:.4f}')

# %%
# Page 36, formulae #141, Page 35, formulae #137
# Formulae 141, 137
# -----------------
# `Page 35, 36`
#
# * :math:`sin(I) -5/4 \times sin^3(I) = 0.3192`
# * :math:`f(141) = sin(I) - 5/4 \times sin^3(i) / 0.3192`

# %%
# .. math::
#
# sin(I) -5/4 \times sin^3(I) = 0.3192
#
# .. math::
#
# f(141) = sin(I) - 5/4 \times sin^3(i) / 0.3192
a141 = math.sin(const.w) - 5 / 4 * math.sin(const.w)**3
print(f'a141 = {a141:.4f}')

# %%
# Page 36, formulae #149, Page 35, formulae #140
# * :math:`cos^6(\frac{1}{2}I) + cos^4(\frac{1}{2}I) \times sin^2(\frac{1}{2}I)`
# * :math:`f(M_3) = cos^6(\frac{1}{2}I) / 0.8758`

# %%
# Page 41, formulae #207, Page 41, formulae #195
# Formulae 149, 140
# -----------------
# `Page 35, 36`
#
# .. math::
#
# cos^6(\frac{1}{2}I) + cos^4(\frac{1}{2}I) \times sin^2(\frac{1}{2}I)
#
# * .. math::
# .. math::
#
# f(M_3) = cos^6(\frac{1}{2}I) / 0.8758
#
# Formulae 207, 195
# -----------------
# `Page 41`
#
# .. math::
#
# 1/Q_a = \left[1/4 + 3/2\frac{cos I}{cos^2 \frac{1}{2}I}\times cos 2P +
# 9/4\frac{cos^2 I}{cos^4 \frac{1}{2} I}\right]^\frac{1}{2}
#
# * :math:`1/Q_a = \left(2.310 + 1.435 \times cos(2P)\right)^\frac{1}{2}`
# * :math:`cos(2P) = cos(2 \times (p - \xi))`
# * :math:`f(M_ 1) = f(O_ 1) \times 1 / Q_a`

# %%
# .. math::
#
# 1/Q_a = \left(2.310 + 1.435 \times cos(2P)\right)^\frac{1}{2}
#
# .. math::
#
# cos(2P) = cos(2 \times (p - \xi))
#
# .. math::
#
# f(M_ 1) = f(O_ 1) \times 1 / Q_a
a195_1 = (1 /
4) + (9 / 4) * (math.cos(const.w)**2 / math.cos(0.5 * const.w)**4)
a195_2 = (3 / 2) * (math.cos(const.w) / math.cos(0.5 * const.w)**2)
print(f'a195_1 = {a195_1:.3f}')
print(f'a195_2 = {a195_2:.3f}')

# %%
# Page 45, formulae 216 & 218, 217, 219
# Formulae 216, 218, 217, 219
# ---------------------------
# `Page 45`
#
# * :math:`1/2 + 3/4 \times e^2 = 0.5023`
# * :math:`(1/2 + 3/4 \times e_1^2) \times S' \times sin(2\omega) = 0.1681`
# * :math:`(1/2 + 3/4 \times e_1^2) \times S' \times sin^2(\omega) = 0.0365`

# %%
# .. math::
#
# 1/2 + 3/4 \times e^2 = 0.5023
#
# .. math::
#
# (1/2 + 3/4 \times e_1^2) \times S' \times sin(2\omega) = 0.1681
#
# .. math::
#
# (1/2 + 3/4 \times e_1^2) \times S' \times sin^2(\omega) = 0.0365
term_a22 = 1 / 2 + 3 / 4 * const.e**2
term_b22 = (1 / 2 + 3 / 4 * const.e1**2) * const.s * math.sin(2 * const.w)
term_a47 = 1 / 2 + 3 / 4 * const.e**2
Expand All @@ -268,70 +337,69 @@ def astronomic_constants() -> AstronomicConstants:
print(f'term B47 = {term_b47:.4f}')

# %%
# Page #45, formulae #226
# Formulae 226
# ------------
# `Page 45`
#
# * .. math::
# .. math::
#
# \left[(A^2 + 2AB \times cos(\upsilon) + B^2)^\frac{1}{2} \times
# cos(\upsilon')\right]_0
# [(A^2 + 2AB \times cos(\upsilon) + B^2)^\frac{1}{2} \times
# cos(\upsilon')]_0
#
# * :math:`\left[0.5023 \times sin(2I) cos(\upsilon) + 0.1681\right]_0 = 0.5305`

# %%
# .. math::
#
# \left[0.5023 \times sin(2I) cos(\upsilon) + 0.1681\right]_0 = 0.5305
a226 = (term_a22 * a68 + term_b22)
print(f'a226 = {a226:.4f}')

# %%
# Page #45, formulae #227
# Formulae 227
# ------------
# `Page 45`
#
# * .. math::
# .. math::
#
# f(K_1) = (0.2523 \times sin^2(2I) + 0.1689 \times sin(2I) \times
# cos(\upsilon) + 0.0283)^\frac{1}{2}/0.5305
#
# * .. math::
# .. math::
#
# f(K_1) = (0.8965 \times sin^2(2I) + 0.6001 \times sin(2I) \times
# cos(\upsilon) + 0.1006)^\frac{1}{2}
#

# %%
print(f'{(term_a22** 2) / a226**2:.4f}')
print(f'{(term_a22 * term_b22 * 2) / a226**2:.4f}')
print(f'{term_b22**2 / a226**2:.4f}')
print(f'{(term_a22 ** 2) / a226 ** 2:.4f}')
print(f'{(term_a22 * term_b22 * 2) / a226 ** 2:.4f}')
print(f'{term_b22 ** 2 / a226 ** 2:.4f}')

# %%
# Page #46, formulae #234
# Formulae 234
# ------------
# `Page 46`
#
# * .. math::
# .. math::
#
# \left[(A^2 + 2AB \times cos(2\upsilon) + B^2)^\frac{1}{2} \times
# cos(\upsilon')\right]_0
# [(A^2 + 2AB \times cos(2\upsilon) + B^2)^\frac{1}{2} \times
# cos(\upsilon')]_0
#
# * .. math::
# .. math::
#
# \left[0.5023 \times sin^2(2I) cos(\upsilon) + 0.0365\right]_0 = 0.1151
#

# %%
a234: float = (term_a47 * a71 + term_b47)
print(f'a226 = {a234:.4f}')

# %%
# Page #46, formulae #235
# Formulae 235
# ------------
# `Page 46`
#
# * .. math::
# .. math::
#
# f(K_2) = (0.2523 \times sin^4(I) + 0.0367 \times sin^2(I) \times
# cos(2\upsilon) + 0.0013)^\frac{1}{2}/0.1151
#
# * .. math::
# .. math::
#
# f(K_2) = (19.0444 \times sin^4(I) + 2.7702 \times sin^2(I) \times
# cos(2\upsilon) + 0.0981)^\frac{1}{2}
#

# %%
print(f'{(term_a47** 2) / a234**2:.4f}')
print(f'{term_a47**2 / a234**2:.4f}')
print(f'{(term_a47 * term_b47 * 2) / a234**2:.4f}')
print(f'{term_b47**2 / a234**2:.4f}')

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