# -*- coding: utf-8 -*-
# PyPlanets: Object-oriented refactoring of PyMeeus, a Python library implementing astronomical algorithms.
# Copyright (C) 2020 Martin Fünffinger
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from math import sqrt, radians, sin, cos, tan, atan
from pyplanets.core.angle import Angle
"""
.. module:: Ellipsoid
:synopsis: Class to model an ellipsoid.
:license: GNU Lesser General Public License v3 (LGPLv3)
.. moduleauthor:: Martin Fünffinger
"""
[docs]class Ellipsoid(object):
"""
Class Ellipsoid is useful to encapsulate the most important parameters of
a given reference ellipsoid.
"""
[docs] def __init__(self, a, f, omega):
"""Ellipsoid constructor.
:param a: Semi-major or equatorial radius, in meters
:type a: float
:param f: Flattening
:type f: float
:param omega: Angular velocity of the Earth, in rad/s
:type omega: float
"""
self._a = a
self._f = f
self._omega = omega
[docs] def __str__(self):
"""Method used when trying to print the object.
:returns: Semi-major equatorial radius, flattening and angular velocity
as a string.
:rtype: string
>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> print(a)
6378140.0:0.0033528132:7.292e-05
"""
return "{}:{}:{}".format(self._a, self._f, self._omega)
[docs] def __repr__(self):
"""Method providing the 'official' string representation of the object.
It provides a valid expression that could be used to recreate the
object.
:returns: As string with a valid expression to recreate the object
:rtype: string
>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> repr(a)
'Ellipsoid(6378140.0, 0.0033528132, 7.292e-05)'
"""
return "{}({}, {}, {})".format(
self.__class__.__name__, self._a, self._f, self._omega
)
[docs] def b(self):
"""Method to return the semi-minor radius.
:returns: Semi-minor radius, in meters
:rtype: float
>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> round(a.b(), 3)
6356755.288
"""
return self._a * (1.0 - self._f)
[docs] def e(self):
"""Method to return the eccentricity of the Earth's meridian.
:returns: Eccentricity of the Earth's meridian
:rtype: float
>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> round(a.e(), 8)
0.08181922
"""
f = self._f
return sqrt(2.0 * f - f * f)
[docs] def rho(self, latitude):
"""Method to compute the rho term, which is the observer distance to
the center of the Earth, when the observer is at sea level. In this
case, the Earth's equatorial radius is taken as unity.
:param latitude: Geodetical or geographical latitude of the observer,
in degrees
:type latitude: int, float, :class:`Angle`
:returns: Rho: Distance to the center of the Earth from sea level. It
is a ratio with respect to Earth equatorial radius.
:rtype: float
:raises: TypeError if input value is of wrong type.
>>> e = IAU76
>>> round(e.rho(0.0), 1)
1.0
"""
if not isinstance(latitude, (int, float, Angle)):
raise TypeError("Invalid input value")
if isinstance(latitude, (int, float)):
phi = radians(latitude) # Convert to radians
else:
phi = latitude.rad() # It is an Angle. Call method rad()
return (0.9983271 + 0.0016764 * cos(2.0 * phi) -
0.0000035 * cos(4.0 * phi))
[docs] def rho_sinphi(self, latitude, height):
"""Method to compute the rho*sin(phi') term, needed in the calculation
of diurnal parallaxes, eclipses and occulatitions.
:param latitude: Geodetical or geographical latitude of the observer,
in degrees
:type latitude: int, float, :class:`Angle`
:param height: Height of the observer above the sea level, in meters
:type height: int, float
:returns: rho*sin(phi') term
:rtype: float
:raises: TypeError if input value is of wrong type.
>>> lat = Angle(33, 21, 22.0)
>>> e = IAU76
>>> round(e.rho_sinphi(lat, 1706), 6)
0.546861
"""
if not (
isinstance(latitude, (int, float, Angle))
and isinstance(height, (int, float))
):
raise TypeError("Invalid input value")
if isinstance(latitude, (int, float)):
phi = radians(latitude) # Convert to radians
else:
phi = latitude.rad() # It is an Angle. Call method rad()
b_a = self.b() / self._a
u = atan(b_a * tan(phi))
return b_a * sin(u) + height / self._a * sin(phi)
[docs] def rho_cosphi(self, latitude, height):
"""Method to compute the rho*cos(phi') term, needed in the calculation
of diurnal parallaxes, eclipses and occulatitions.
:param latitude: Geodetical or geographical latitude of the observer,
in degrees
:type latitude: int, float, :class:`Angle`
:param height: Height of the observer above the sea level, in meters
:type height: int, float
:returns: rho*cos(phi') term
:rtype: float
:raises: TypeError if input value is of wrong type.
>>> lat = Angle(33, 21, 22.0)
>>> e = IAU76
>>> round(e.rho_cosphi(lat, 1706), 6)
0.836339
"""
if not (
isinstance(latitude, (int, float, Angle))
and isinstance(height, (int, float))
):
raise TypeError("Invalid input value")
if isinstance(latitude, (int, float)):
phi = radians(latitude) # Convert to radians
else:
phi = latitude.rad() # It is an Angle. Call method rad()
b_a = self.b() / self._a
u = atan(b_a * tan(phi))
return cos(u) + height / self._a * cos(phi)
[docs] def rp(self, latitude):
"""Method to compute the radius of the parallel circle at the given
latitude.
:param latitude: Geodetical or geographical latitude of the observer,
in degrees
:type latitude: int, float, :class:`Angle`
:returns: Radius of the parallel circle at given latitude, in meters
:rtype: float
:raises: TypeError if input value is of wrong type.
>>> e = IAU76
>>> round(e.rp(42.0), 1)
4747001.2
"""
if not isinstance(latitude, (int, float, Angle)):
raise TypeError("Invalid input value")
if isinstance(latitude, (int, float)):
phi = radians(latitude) # Convert to radians
else:
phi = latitude.rad() # It is an Angle. Call method rad()
a = self._a
e = self.e()
return (a * cos(phi)) / sqrt(1.0 - e * e * sin(phi) * sin(phi))
[docs] def linear_velocity(self, latitude):
"""Method to compute the linear velocity of a point at latitude, due
to the rotation of the Earth.
:param latitude: Geodetical or geographical latitude of the observer,
in degrees
:type latitude: int, float, :class:`Angle`
:returns: Linear velocity of a point at latitude, in meters per second
:rtype: float
:raises: TypeError if input value is of wrong type.
>>> e = IAU76
>>> round(e.linear_velocity(42.0), 2)
346.16
"""
if not isinstance(latitude, (int, float, Angle)):
raise TypeError("Invalid input value")
omega = self._omega
return omega * self.rp(latitude)
[docs] def rm(self, latitude):
"""Method to compute the radius of curvature of the Earth's meridian
at the given latitude.
:param latitude: Geodetical or geographical latitude of the observer,
in degrees
:type latitude: int, float, :class:`Angle`
:returns: Radius of curvature of the Earth's meridian at the given
latitude, in meters
:rtype: float
:raises: TypeError if input value is of wrong type.
>>> e = IAU76
>>> round(e.rm(42.0), 1)
6364033.3
"""
if not isinstance(latitude, (int, float, Angle)):
raise TypeError("Invalid input value")
if isinstance(latitude, (int, float)):
phi = radians(latitude) # Convert to radians
else:
phi = latitude.rad() # It is an Angle. Call method rad()
a = self._a
e = self.e()
return (a * (1.0 - e * e)) / (1.0 - e * e * sin(phi) * sin(phi)) ** 1.5
[docs] def distance(self, lon1, lat1, lon2, lat2):
"""This method computes the distance between two points on the Earth's
surface using the method from H. Andoyer.
.. note:: We will consider that positions 'East' and 'South' are
negative.
:param lon1: Longitude of the first point, in degrees
:type lon1: int, float, :class:`Angle`
:param lat1: Geodetical or geographical latitude of the first point,
in degrees
:type lat1: int, float, :class:`Angle`
:param lon2: Longitude of the second point, in degrees
:type lon2: int, float, :class:`Angle`
:param lat2: Geodetical or geographical latitude of the second point,
in degrees
:type lat2: int, float, :class:`Angle`
:returns: Tuple with distance between the two points along Earth's
surface, and approximate error, in meters
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> e = IAU76
>>> lon1 = Angle(-2, 20, 14.0)
>>> lat1 = Angle(48, 50, 11.0)
>>> lon2 = Angle(77, 3, 56.0)
>>> lat2 = Angle(38, 55, 17.0)
>>> dist, error = e.distance(lon1, lat1, lon2, lat2)
>>> round(dist, 0)
6181628.0
>>> error
69.0
>>> lon1 = Angle(-2.09)
>>> lat1 = Angle(41.3)
>>> lon2 = Angle(73.99)
>>> lat2 = Angle(40.75)
>>> dist, error = e.distance(lon1, lat1, lon2, lat2)
>>> round(dist, 0)
6176760.0
>>> error
69.0
"""
if not (
isinstance(lon1, (int, float, Angle))
and isinstance(lat1, (int, float, Angle))
and isinstance(lon2, (int, float, Angle))
and isinstance(lat2, (int, float, Angle))
):
raise TypeError("Invalid input value")
if isinstance(lon1, (int, float)):
l1 = radians(lon1) # Convert to radians
else:
l1 = lon1.rad() # It is an Angle. Call method rad()
if isinstance(lat1, (int, float)):
phi1 = radians(lat1) # Convert to radians
else:
phi1 = lat1.rad() # It is an Angle. Call method rad()
if isinstance(lon2, (int, float)):
l2 = radians(lon2) # Convert to radians
else:
l2 = lon2.rad() # It is an Angle. Call method rad()
if isinstance(lat2, (int, float)):
phi2 = radians(lat2) # Convert to radians
else:
phi2 = lat2.rad() # It is an Angle. Call method rad()
f = (phi1 + phi2) / 2.0
g = (phi1 - phi2) / 2.0
lam = (l1 - l2) / 2.0
sin2g = sin(g) ** 2
cos2g = cos(g) ** 2
cos2f = cos(f) ** 2
sin2f = sin(f) ** 2
sin2lam = sin(lam) ** 2
cos2lam = cos(lam) ** 2
s = sin2g * cos2lam + cos2f * sin2lam
c = cos2g * cos2lam + sin2f * sin2lam
omega = atan(sqrt(s / c))
r = sqrt(s * c) / omega
d = 2.0 * omega * self._a
h1 = (3.0 * r - 1.0) / (2.0 * c)
h2 = (3.0 * r + 1.0) / (2.0 * s)
fe = self._f
dist = d * (1.0 + fe * (h1 * sin2f * cos2g - h2 * cos2f * sin2g))
error = round(dist * fe * fe, 0)
return dist, error
IAU76 = Ellipsoid(6378140.0, (1.0 / 298.257), 7.292114992e-5)
"""Reference ellipsoid defined by the International Astronomic Union in 1976"""
WGS84 = Ellipsoid(6378137.0, (1.0 / 298.257223563), 7292115e-11)
"""Reference ellipsoid World Geodetic System 1984, a modern ellipsoid used by
the GPS system, and the standard in many applications"""