The Moon has mass and radius .

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

The Moon has mass 7.3×1022 kg7.3\times10^{22}\,\text{kg} and radius 1.7×106 m1.7\times10^{6}\,\text{m}. (i) Calculate the escape velocity from the lunar surface. Take G=6.67×10−11 N m2kg−2G = 6.67\times10^{-11}\,\text{N\,m}^2\text{kg}^{-2}. (ii) A probe of mass 500 kg500\,\text{kg} is launched straight up from the Moon with an initial speed of 2.0 km s−12.0\,\text{km\,s}^{-1}. Determine whether the probe will escape the Moon’s gravity, giving reasons. (iii) If the probe does not escape, compute the maximum height above the lunar surface it will reach before momentarily coming to rest. Neglect the gravitational influence of any other body.

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