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The first lunar probe to successfully touch down on the lunar surface was Luna 2. It was launched in 1959 with a mass of 320.9 kg. Consider the following 4 locations on its journey to the Moon. All positions are from the Earth center.
(near earth) 7x10^6m
(midway) 1.92x10^8m
(Lagrange point) 3.46x10^8m
(near moon) 3.82x10^8m
(a) Find the force of gravity from the Earth on Luna 2 at these points. The mass of the Earth is 5.97×1024 kg.
(b) Find the force of gravity on Luna 2 by the Moon at these points. Let the distance from the Earth to the moon be use 3.84×108 m and the mass of the Moon is 7.35×1022 kg.
(c) Find the total weight of Luna 2 due to both the Earth and the Moon at these points. Remember that Luna 2 is in-between them.
(d) Based on your results in (c), what is the significance of the "Lagrange point?"
Show all the steps in the mechanism for the following reaction, When benzene is mixed with deuterated sulfuric acid, deuterium is slowly incorporated onto the ring. Show the mechanism for this reaction and explain how this relates the sulfonation of ..
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