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20 Physics -- Gravitation

Which takes more fuel, a voyage from the earth to the moon or from the moon to the earth? 

Which takes more fuel, a voyage from the earth to the moon or from the moon to the earth? 

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The gravitational potential energy of a voyager of mass m at a distance r from the earth is where M is the mass of the earth. The gravitational potential energy of the voyager at a distance r from the moon is where Mmoon is the mass of the moon. As r and m are constants and M > Mmoon, then numerically, W > Wmoon, i.e. the work needed to make a voyage from the earth to the moon is greater than that from the moon to the earth. So it takes more fuel to make the voyage from the earth to the moon 

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