TheAlgorithms · MaximSmolskiy · May 10, 2025 · May 6, 2025 · May 6, 2025 · May 6, 2025
diff --git a/physics/escape_velocity.py b/physics/escape_velocity.py
@@ -0,0 +1,67 @@
+import math
+
+
+def escape_velocity(mass: float, radius: float) -> float:
+    """
+    Calculates the escape velocity needed to break free from a celestial body's
+    gravitational field.
+
+    The formula used is:
+        v = sqrt(2 * G * M / R)
+
+    where:
+        v = escape velocity (m/s)
+        G = gravitational constant (6.67430 * 10^-11 m^3 kg^-1 s^-2)
+        M = mass of the celestial body (kg)
+        R = radius from the center of mass (m)
+
+    Source:
+        https://en.wikipedia.org/wiki/Escape_velocity
+
+    Args:
+        mass (float): Mass of the celestial body in kilograms.
+        radius (float): Radius from the center of mass in meters.
+
+    Returns:
+        float: Escape velocity in meters per second, rounded to 3 decimal places.
+
+    Examples:
+        >>> escape_velocity(mass=5.972e24, radius=6.371e6)  # Earth
+        11185.978
+        >>> escape_velocity(mass=7.348e22, radius=1.737e6)  # Moon
+        2376.307
+        >>> escape_velocity(mass=1.898e27, radius=6.9911e7)  # Jupiter
+        60199.545
+        >>> escape_velocity(mass=0, radius=1.0)
+        0.0
+        >>> escape_velocity(mass=1.0, radius=0)
+        Traceback (most recent call last):
+            ...
+        ZeroDivisionError: Radius cannot be zero.
+    """
+    gravitational_constant = 6.67430e-11  # m^3 kg^-1 s^-2
+
+    if radius == 0:
+        raise ZeroDivisionError("Radius cannot be zero.")
+
+    velocity = math.sqrt(2 * gravitational_constant * mass / radius)
+    return round(velocity, 3)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print("Calculate escape velocity of a celestial body...\n")
+
+    try:
+        mass = float(input("Enter mass of the celestial body (in kgs): ").strip())
+        radius = float(input("Enter radius from the center of mass (in ms): ").strip())
+
+        velocity = escape_velocity(mass=mass, radius=radius)
+        print(f"Escape velocity is {velocity} m/s")
+
+    except ValueError:
+        print("Invalid input. Please enter valid numeric values.")
+    except ZeroDivisionError as e:
+        print(e)