Relativistic velocity summation function

physics/relativistic_velocity_summation.py

@@ -0,0 +1,47 @@
+"""
+The relativistic velocity summation formula calculates the combined velocity v2
+of an object moving at speed v1 relative to a frame that is itself moving at velocity v
+relative to an observer. I take the last one to be strictly lower than the speed of
+light.
+The formula is v2 = (v1 + v)/(1 + v1 * v / c**2)
+v1 - speed of the object relative to a moving frame
+v - speed of the moving frame
+c - speed of light in the vacuum
+v2 - speed of the object relative to an observer
+"""
+
+c = 299792458
+
+
+def relativistic_velocity_summation(
+    object_velocity: float, frame_velocity: float
+) -> float:
+    """
+    >>> relativistic_velocity_summation(200000000, 200000000)
+    276805111.0636436
+    >>> relativistic_velocity_summation(299792458, 100000000)
+    299792458.0
+    >>> relativistic_velocity_summation(100000000, 299792458)
+    Traceback (most recent call last):
+        ...
+    ValueError: Speeds must not exceed light speed...
+    """
+    if (
+        object_velocity > c
+        or frame_velocity >= c
+        or object_velocity < -c
+        or frame_velocity <= -c
+    ):
+        raise ValueError(
+            "Speeds must not exceed light speed, and "
+            "the frame speed must be lower than the light speed!"
+        )
+    numerator = object_velocity + frame_velocity
+    denominator = 1 + object_velocity * frame_velocity / c**2
+    return numerator / denominator
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()