Problem: Consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and of such a force are given by Newton's law of gravity:F→G=-Gm1m2r2r→,whereds→=drr^; G, m1, and m2 are constants; and r>0.FindU(rf)-U(r0)=∫r0rfFG→·ds→,Express your answer in terms of G, m1, m2, r0, and rf.

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Problem Details

Consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and of such a force are given by Newton's law of gravity:

FG=-Gm1m2r2r,

where

ds=drr^; G, m1, and m2 are constants; and r>0.

Find

U(rf)-U(r0)=r0rfFG·ds,

Express your answer in terms of G, m1, m2, r0, and rf.

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