Two objects have masses of 6 MG and 8 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 340 m to 160 m?

1 Answer
David G.
Jul 20, 2017

At 340 m the gravitational potential energy between the masses is −9.4×10−6 J and at 160 m it is 2.0×10−5 J.

The change is −1.91×10−5 J.

Explanation:

Note that "mg" is a milligram, 10−3 g, but MG is a megagram, 106 g. This is equal to 103 kg, and since kg is the SI unit and the gravitational constant is expressed in terms of it, that is the unit we will use.

U=−Gm1m2r where G=6.67×10−11 m3kg−1s−2

At 340 m:

U=−Gm1m2r=−6.67×10−11×6×103×8×103340

=−3.2×10−3340=−9.4×10−6J

At 160 m:

U=−Gm1m2r=−6.67×10−11×6×103×8×103160

=−3.2×10−3160=−2.0×10−5J

The change is (final-initial) =−2.0×10−5−(−9.4×10−6)=−1.91×10−5 J

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