diff --git a/physics/orbital_transfer_work.py b/physics/orbital_transfer_work.py new file mode 100644 index 000000000000..7fb90fe9be0e --- /dev/null +++ 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}")