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