Answer to Question #253089 in Physics for Inday

Question #253089

An unknown planet has mass 20 times that of the Earth and 20 times of its radius. If Pedro is weighing 700N on  

Earth, what would be his weight on this new planet?



1
Expert's answer
2021-10-19T15:16:18-0400

Express the acceleration due to gravity in terms of planet mass and radius using the law of universal gravitation:


mg=GMm/R2,g=GM/R2.mg=GMm/R^2,\\ g=GM/R^2.

On earth:


W1=mg1m=W1g1.W_1=mg_1→m=\frac{W_1}{g_1}.

On another planet:


W2=mg2=G(20M)m/(20R2), W2=W120/400=35 N.W_2=mg_2=G(20M)m/(20R^2),\\\space\\ W_2=W_1·20/400=35\text{ N}.


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