Merge 4bf840e into 1e4a4a1

fatiando/gravmag/normal_gravity.py

@@ -0,0 +1,126 @@
+"""
+Gravity of ellipsoid models and common reductions (Bouguer, free-air)
+
+**Reference ellipsoids**
+
+This module uses instances of
+:class:`~fatiando.gravmag.normal_gravity.ReferenceEllipsoid` to store the
+physical constants of ellipsoids.
+To create a new ellipsoid, just instantiate ``ReferenceEllipsoid`` and give it
+the semimajor axis ``a``, the flattening ``f``, the geocentric gravitational
+constant ``GM``, and the angular velocity ``omega``.
+All  other quantities, like the gravity at the poles and equator,
+eccentricities, etc, are computed by the class from these 4 parameters.
+
+Available ellipsoids:
+
+* ``WGS84``::
+
+    >>> from fatiando.gravmag.normal_gravity import WGS84
+    >>> print('{:.0f}'.format(WGS84.a))
+    6378137
+    >>> print('{:.17f}'.format(WGS84.f))
+    0.00335281066474748
+    >>> print('{:.10g}'.format(WGS84.GM))
+    3.986004418e+14
+    >>> print('{:.7g}'.format(WGS84.omega))
+    7.292115e-05
+    >>> print('{:.4f}'.format(WGS84.b))
+    6356752.3142
+    >>> print('{:.8f}'.format(WGS84.E)) # Linear eccentricity
+    521854.00842339
+    >>> print('{:.15f}'.format(WGS84.e_prime)) # second eccentricity
+    0.082094437949696
+    >>> print('{:.10f}'.format(WGS84.gamma_a)) # gravity at the equator
+    9.7803253359
+    >>> print('{:.11f}'.format(WGS84.gamma_b)) # gravity at the pole
+    9.83218493786
+    >>> print('{:.14f}'.format(WGS84.m))
+    0.00344978650684
+
+
+"""
+from __future__ import division
+import math
+
+
+class ReferenceEllipsoid(object):
+    """
+    A generic reference ellipsoid.
+
+    It stores the physical constants defining the ellipsoid and has properties
+    for computing other (derived) quantities.
+
+    All quantities are expected and returned in SI units.
+
+    Parameters:
+
+    * a : float
+        The semimajor axis (the largest one, at the equator). In meters.
+    * f : float
+        The flattening. Adimensional.
+    * GM : float
+        The geocentric gravitational constant of the earth, including the
+        atmosphere. In :math:`m^3 s^{-2}`.
+    * omega : float
+        The angular velocity of the earth. In :math:`rad s^{-1}`.
+
+    """
+
+    def __init__(self, a, f, GM, omega):
+        self._a = a
+        self._f = f
+        self._GM = GM
+        self._omega = omega
+
+    @property
+    def a(self):
+        return self._a
+
+    @property
+    def f(self):
+        return self._f
+
+    @property
+    def GM(self):
+        return self._GM
+
+    @property
+    def omega(self):
+        return self._omega
+
+    @property
+    def b(self):
+        return self.a*(1 - self.f)
+
+    @property
+    def E(self):
+        return math.sqrt(self.a**2 - self.b**2)
+
+    @property
+    def e_prime(self):
+        return self.E/self.b
+
+    @property
+    def m(self):
+        return (self.omega**2)*(self.a**2)*self.b/self.GM
+
+    @property
+    def gamma_a(self):
+        bE = self.b/self.E
+        atanEb = math.atan2(self.E, self.b)
+        q0 = 0.5*((1 + 3*bE**2)*atanEb - 3*bE)
+        q0prime = 3*(1 + bE**2)*(1 - bE*atanEb) - 1
+        m = self.m
+        return self.GM*(1 - m - m*self.e_prime*q0prime/(6*q0))/(self.a*self.b)
+
+    @property
+    def gamma_b(self):
+        bE = self.b/self.E
+        atanEb = math.atan2(self.E, self.b)
+        q0 = 0.5*((1 + 3*bE**2)*atanEb - 3*bE)
+        q0prime = 3*(1 + bE**2)*(1 - bE*atanEb) - 1
+        return self.GM*(1 + self.m*self.e_prime*q0prime/(3*q0))/self.a**2
+
+WGS84 = ReferenceEllipsoid(a=6378137, f=1/298.257223563, GM=3986004.418e8,
+                           omega=7292115e-11)