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A satellite of mass 200 kg moves in a circular orbit around the Earth…
Question
A satellite of mass 200 kg moves in a circular orbit around the Earth at a height equal to the Earth's radius above the surface (so its orbital radius is twice the Earth's radius). Take the Earth's radius as 6.4 x 10^6 m and surface gravity g = 10 m/s^2. Find the minimum additional energy (in joules) that must be supplied to the satellite to just allow it to escape to infinity from this orbit.
✓ Verified answer: 3200000000checked by our engine — not a guess
Step-by-step solution
GM = gR^2.
Total mechanical energy of a circular orbit of radius r is E = -GMm/(2r).
With r = 2R, E_orbit = -GMm/(4R).
Energy to reach infinity (E_infinity = 0) is the orbit's binding energy = +GMm/(4R) = g R^2 m/(4R) = g R m/4 = 10 * 6.4e6 * 200 / 4 = 3.2 x 10^9 J.
Final answer3200000000
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