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Answer :
The satellite-Earth system's gravitational potential energy is approximately -4.45 × 10⁹ joules, determined by the masses of the satellite and Earth, and their separation distance.
Gravitational Potential Energy of a Satellite -
To calculate the potential energy of the satellite-Earth system, we use the formula for gravitational potential energy (U):
U = - (G * M * m) / r
Here, G is the gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²), M is the mass of the Earth (5.97 × 10²⁴ kg), m is the mass of the satellite (93 kg), and r is the distance from the center of the Earth to the satellite.
The radius of the Earth is 6.371 × 10⁶ m, so the total distance r is:
r = 6.371 × 10⁶ m + 1.95 × 10⁶ m = 8.321 × 10⁶ m.
Plugging in the values:
U = - (6.67 × 10⁻¹¹ Nm²/kg² * 5.97 × 10²⁴ kg * 93 kg) / 8.321 × 10⁶ m
After calculating, we get:
U ≈ - 4.45 × 10⁹ J
Thus, the gravitational potential energy of the satellite-Earth system is approximately -4.45 × 10⁹ joules.
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