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Zero, a hypothetical planet, has a mass of \( 5.0 \times 10^{23} \mathrm{~kg} \), a radius of \( 3.5 \times 10^{6} \mathrm{~m} \), and no atmosphere. A \( 10 \mathrm{~kg} \) space probe is to be launched vertically from its surface.
If the probe is to achieve a maximum distance of \( 8.0 \times 10^{6} \mathrm{~m} \) from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?
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