# Source code for boule.sphere

# Copyright (c) 2019 The Boule Developers.
# Distributed under the terms of the BSD 3-Clause License.
#
# This code is part of the Fatiando a Terra project (https://www.fatiando.org)
#
"""
Define the reference sphere (ellipsoid with 0 flattening).
"""
from warnings import warn

import attr
import numpy as np

from .ellipsoid import Ellipsoid

# Don't let ellipsoid parameters be changed to avoid messing up calculations
# accidentally.
[docs]@attr.s(frozen=True)
class Sphere(Ellipsoid):
"""
Reference sphere (zero flattening ellipsoids)

Represents a rotating reference ellipsoid with zero flattening. It is
defined by three parameters (radius, geocentric gravitational constant, and
angular velocity) and offers other derived quantities.

**All attributes of this class are read-only and cannot be changed after
instantiation.**

All parameters are in SI units.

.. note::

Must be used instead of :class:boule.Ellipsoid to account for
singularities due to zero flattening (and thus zero eccentricity) in
normal gravity calculations.

Parameters
----------
name : str
A short name for the sphere, for example 'Moon'.
The radius of the sphere [meters].
geocentric_grav_const : float
The geocentric gravitational constant (GM) [m^3 s^-2].
angular_velocity : float
The angular velocity of the rotating sphere (omega) [rad s^-1].
long_name : str or None
A long name for the sphere, for example "Moon Reference System"
(optional).
reference : str or None
Citation for the sphere parameter values (optional).

Examples
--------

We can define a sphere by specifying the 3 key numerical parameters:

>>> sphere = Sphere(
...     name="Moon",
...     long_name="That's no moon",
...     geocentric_grav_const=2,
...     angular_velocity=0.5,
... )
>>> print(sphere) # doctest: +ELLIPSIS
Sphere(name='Moon', ...)
>>> print(sphere.long_name)
That's no moon

The class defines several derived attributes based on the input parameters:

>>> print("{:.2f}".format(sphere.semimajor_axis))
1.00
>>> print("{:.2f}".format(sphere.semiminor_axis))
1.00
1.00
>>> print("{:.2f}".format(sphere.gravity_equator))
1.75
>>> print("{:.2f}".format(sphere.gravity_pole))
2.00

Normal gravity (the magnitude of the gravity potential) can be calculated
at any latitude and height. **Note that this method returns values in mGal

>>> print("{:.2f}".format(sphere.normal_gravity(latitude=0, height=0)))
175000.00
>>> print("{:.2f}".format(sphere.normal_gravity(latitude=90, height=0)))
200000.00

The flag si_units will return the Normal gravity in m/s².

>>> print("{:.2f}".format(sphere.normal_gravity(latitude=0, height=0, si_units=True)))
1.75
>>> print("{:.2f}".format(sphere.normal_gravity(latitude=90, height=0, si_units=True)))
2.00

The flattening and eccentricities will all be zero:

>>> print("{:.2f}".format(sphere.flattening))
0.00
>>> print("{:.2f}".format(sphere.linear_eccentricity))
0.00
>>> print("{:.2f}".format(sphere.first_eccentricity))
0.00
>>> print("{:.2f}".format(sphere.second_eccentricity))
0.00

"""

name = attr.ib()
geocentric_grav_const = attr.ib()
angular_velocity = attr.ib()
long_name = attr.ib(default=None)
reference = attr.ib(default=None)
# semimajor_axis and flattening shouldn't be defined on initialization:
#   - semimajor_axis will be equal to radius
#   - flattening will be equal to zero
semimajor_axis = attr.ib(init=False, repr=False)
flattening = attr.ib(init=False, default=0, repr=False)

@semimajor_axis.default
def _set_semimajor_axis(self):
"The semimajor axis should be the radius"

):  # pylint: disable=no-self-use,unused-argument
"""
Check if the radius is positive
"""
if not value > 0:
raise ValueError(f"Invalid radius '{value}'. Should be greater than zero.")

@geocentric_grav_const.validator
def _check_geocentric_grav_const(
self, geocentric_grav_const, value
):  # pylint: disable=no-self-use,unused-argument
"""
Warn if geocentric_grav_const is negative
"""
if value < 0:
warn(f"The geocentric gravitational constant is negative: '{value}'")

[docs]    def normal_gravity(self, latitude, height, si_units=False):
r"""
Calculate normal gravity at any latitude and height

Computes the magnitude of the gradient of the gravity potential
(gravitational + centrifugal; see [Heiskanen-Moritz]_) generated by the
sphere at the given latitude :math:\theta and height :math:h:

.. math::

\gamma(\theta, h) =
\sqrt{\left( \frac{GM}{(R + h)^2} \right)^2
+ \left(\omega^2 (R + h) - 2\frac{GM}{(R + h)^2} \right)
\omega^2 (R + h) \cos^2 \theta}

in which :math:R is the sphere radius, :math:G is the gravitational
constant, :math:M is the mass of the sphere, and :math:\omega is
the angular velocity.

.. note::

A sphere under rotation is not in hydrostatic equilibrium.
Therefore, it is not it's own equipotential gravity surface (as is
the case for the ellipsoid) and the normal gravity vector is not
normal to the surface of the sphere.

Parameters
----------
latitude : float or array
The latitude where the normal gravity will be computed (in
degrees). For a reference sphere there is no difference between
geodetic and spherical latitudes.
height : float or array
The height (above the surface of the sphere) of the computation
point (in meters).
si_units : bool
Return the value in mGal (False, default) or SI units (True)

Returns
-------
gamma : float or array
The normal gravity in mGal.

"""
# Warn if height is negative
if np.any(height < 0):
warn(
"Formulas used are valid for points outside the ellipsoid."
"Height must be greater than or equal to zero."
)
gravity_acceleration = self.geocentric_grav_const / (radial_distance) ** 2
gamma = np.sqrt(
gravity_acceleration ** 2
+ (self.angular_velocity ** 2 * radial_distance - 2 * gravity_acceleration)
* self.angular_velocity ** 2
# replace cos^2 with (1 - sin^2) for more accurate results on the pole
* (1 - np.sin(np.radians(latitude)) ** 2)
)
if si_units:
return gamma
# Convert gamma from SI to mGal
return gamma * 1e5

@property
def gravity_equator(self):
"""
The norm of the gravity vector at the equator on the sphere [m/s²]

Overrides the inherited method from :class:boule.Ellipsoid to avoid
singularities due to zero flattening.
"""
return (
self.geocentric_grav_const / self.radius ** 2
- self.radius * self.angular_velocity ** 2
)

@property
def gravity_pole(self):
"""
The norm of the gravity vector at the poles on the sphere [m/s²]

Overrides the inherited method from :class:boule.Ellipsoid to avoid
singularities due to zero flattening.
"""
return self.geocentric_grav_const / self.radius ** 2