Add physics script for the light aberration calculation. (#12686)

* Add physics script for the light abberation calculation.

* updating DIRECTORY.md

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: mindaugl

DIRECTORY.md

@@ -1026,6 +1026,7 @@
   * [In Static Equilibrium](physics/in_static_equilibrium.py)
   * [Kinetic Energy](physics/kinetic_energy.py)
   * [Lens Formulae](physics/lens_formulae.py)
+  * [Light Aberration](physics/light_aberration.py)
   * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
   * [Magnetic Flux](physics/magnetic_flux.py)
   * [Malus Law](physics/malus_law.py)

physics/light_aberration.py

@@ -0,0 +1,50 @@
+"""
+Title : Calculate Light Aberration (astronomy)
+
+Description :
+    The below algorithm calculates astronomical light aberration as obtained
+    using Special Relativity.
+
+"""
+
+from math import atan, sqrt, tan
+
+
+def get_aberration_angle(angle_rest: float, velocity_over_c: float) -> float:
+    """
+    This method calculates astronomical light aberration.
+    The angle at rest 'angle_rest' is given in radians [rad]
+    and is in the range (-pi, pi).
+    The relative velocity of observer w.r.t. to the light emitting object is
+    expressed by 'velocity_over_c' that is given as ratio for velocity
+    w.r.t. the speed of light c and is in the range (0, 1).
+
+    https://en.wikipedia.org/wiki/Aberration_(astronomy)
+
+    tan(phi/2) = sqrt((1 - v/c)/(1 + v/c)) * tan(theta/2)
+
+    Where v is the relative velocity, phi is the observed angle with respect to the
+    velocity vector (affected by light aberration), and theta is the angle observed
+    angle in the limit of veclocity being equal to 0.
+
+    Examples:
+    >>> get_aberration_angle(0.2, 0.1)
+    0.18102
+    >>> get_aberration_angle(0.2, 0)
+    0.2
+    >>> get_aberration_angle(0, 0.2)
+    0.0
+    >>> get_aberration_angle(-1.5707963267948966, 0.7)
+    -0.7954
+    """
+
+    factor = sqrt((1 - velocity_over_c) / (1 + velocity_over_c))
+    angle_ab = 2 * atan(factor * tan(angle_rest / 2))
+
+    return round(angle_ab, 5)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()