AlgorithmAndLeetCode · pull · May 13, 2025 · May 13, 2025
diff --git a/physics/orbital_transfer_work.py b/physics/orbital_transfer_work.py
@@ -0,0 +1,73 @@
+def orbital_transfer_work(
+    mass_central: float, mass_object: float, r_initial: float, r_final: float
+) -> str:
+    """
+    Calculates the work required to move an object from one orbit to another in a
+    gravitational field based on the change in total mechanical energy.
+
+    The formula used is:
+        W = (G * M * m / 2) * (1/r_initial - 1/r_final)
+
+    where:
+        W = work done (Joules)
+        G = gravitational constant (6.67430 * 10^-11 m^3 kg^-1 s^-2)
+        M = mass of the central body (kg)
+        m = mass of the orbiting object (kg)
+        r_initial = initial orbit radius (m)
+        r_final = final orbit radius (m)
+
+    Args:
+        mass_central (float): Mass of the central body (kg)
+        mass_object (float): Mass of the object being moved (kg)
+        r_initial (float): Initial orbital radius (m)
+        r_final (float): Final orbital radius (m)
+
+    Returns:
+        str: Work done in Joules as a string in scientific notation (3 decimals)
+
+    Examples:
+        >>> orbital_transfer_work(5.972e24, 1000, 6.371e6, 7e6)
+        '2.811e+09'
+        >>> orbital_transfer_work(5.972e24, 500, 7e6, 6.371e6)
+        '-1.405e+09'
+        >>> orbital_transfer_work(1.989e30, 1000, 1.5e11, 2.28e11)
+        '1.514e+11'
+    """
+    gravitational_constant = 6.67430e-11
+
+    if r_initial <= 0 or r_final <= 0:
+        raise ValueError("Orbital radii must be greater than zero.")
+
+    work = (gravitational_constant * mass_central * mass_object / 2) * (
+        1 / r_initial - 1 / r_final
+    )
+    return f"{work:.3e}"
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print("Orbital transfer work calculator\n")
+
+    try:
+        M = float(input("Enter mass of central body (kg): ").strip())
+        if M <= 0:
+            r1 = float(input("Enter initial orbit radius (m): ").strip())
+        if r1 <= 0:
+            raise ValueError("Initial orbit radius must be greater than zero.")
+
+        r2 = float(input("Enter final orbit radius (m): ").strip())
+        if r2 <= 0:
+            raise ValueError("Final orbit radius must be greater than zero.")
+        m = float(input("Enter mass of orbiting object (kg): ").strip())
+        if m <= 0:
+            raise ValueError("Mass of the orbiting object must be greater than zero.")
+        r1 = float(input("Enter initial orbit radius (m): ").strip())
+        r2 = float(input("Enter final orbit radius (m): ").strip())
+
+        result = orbital_transfer_work(M, m, r1, r2)
+        print(f"Work done in orbital transfer: {result} Joules")
+
+    except ValueError as e:
+        print(f"Input error: {e}")