Zero, a hypothetical planet, has a mass of 2.0 times 10^23 kg, a radius of 3.0 t

Question

Zero, a hypothetical planet, has a mass of 2.0 times 10^23 kg, a radius of 3.0 times 10^6 m. and no atmosphere A l2 kg space probe is to be launched vertically from its surface If the probe is launched with an initial kinetic energy of 5 0 times 10^7,. what will be its kinetic energy when mi4 0timesl0^6m from the center of Zero? If the probe is to achieve a maximum distance of 8 0 times 10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Explanation / Answer

a) Since the gravitational force is a conservative force, the mechanical energy of the probe-planet system is conserved. The energy conservation equation yields

Ei = Ef Ki – GMm/Ri = Kf – GMm/Rf Kf = Ki – GMm(1/Ri – 1/Rf) = 3.68 × 10^7 J

b) When the probe reaches the maximum height, its speed becomes zero. The energy conservation equation leads to Ei = Ef Ki – GMm/Ri = -GMm/Rf Ki = GMm(1/Ri – 1/Rf) = 3.3 × 10^7 J

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