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$${E_{{\rm{pot}}}}\left( {{r_{\rm{E}}}+400\,{\rm{km}}} \right)=-6{,}674 \cdot {10^{-11}}\,\frac{{{{\rm{m}}^3}}}{{{\rm{kg}}\,{{\rm{s}}^2}}} \cdot 500\,{\rm{kg}} \cdot 5{,}972 \cdot {10^{24}}\,{\rm{kg}} \cdot \frac{1}{{6371 \cdot {{10}^3}\,{\rm{m}} + 400 \cdot {{10}^3}\,{\rm{m}}}} =  - 2{,}94 \cdot {10^{10}}\,{\rm{J}}$$

$$f(x) = x * e^{2 pi i \xi x}dasasdasdasdasdasdasdasdasdasdasdasdasdasdasd$$

Lösung

Gegeben:

• Masse des Satelliten ( m )

• Höhe über der Erdoberfläche ( h )

• Gravitationskonstante ( G )

• Masse der Erde ( M )

• Radius der Erde ( R )

$$E_p = -\frac{G \cdot M \cdot m}{R + h}$$

a) Potenzielle Energie, ( E_p ):

[ E_p = -\frac{G \cdot M \cdot m}{R + h} ]

b) Winkelgeschwindigkeit, ( \omega ), und Bahngeschwindigkeit, ( v ):

[ \omega = \sqrt{\frac{G \cdot M}{(R + h)^3}} ] [ v = \omega \cdot (R + h) ]

c) Kinetische Energie, ( E_k ):

[ E_k = \frac{1}{2} \cdot m \cdot v^2 ]

d) Gesamtenergie, ( E_{gesamt} ):

[ E_{gesamt} = E_k + E_p ]

calculates the total energy.

def calculate_total_energy(kinetic_energy, potential_energy):
    return kinetic_energy + potential_energy

# Example usage:
kinetic_energy = 50  # Example value in Joules
potential_energy = 20  # Example value in Joules
total_energy = calculate_total_energy(kinetic_energy, potential_energy)
print(f"Total Energy: {total_energy} Joules")