Two objects have masses of 3 MG3MG and 10 MG10MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 130 m130m to 24 m24m?

1 Answer
Sep 25, 2017

=-6.79*10^-23J=6.791023J

Explanation:

m_1=3MG=3*10^-6 kgm1=3MG=3106kg
m_2=10 MG=10*10^-6 kgm2=10MG=10106kg
"Gravitational Potential Energy"=-(Gm_1m_2)/rGravitational Potential Energy=Gm1m2r
when r=130mr=130m
Potential Energy is U_1=-(Gm_1m_2)/130U1=Gm1m2130
when r=24mr=24m
Potential Energy is U_2=-(Gm_1m_2)/24U2=Gm1m224

Change in Gravitational Potential Energy =U_2-U_1=U2U1
=-(Gm_1m_2)/24-(-(Gm_1m_2)/130)=Gm1m224(Gm1m2130)
=-(Gm_1m_2)/24+(Gm_1m_2)/130=Gm1m224+Gm1m2130
=Gm_1m_2(1/130-1/24)=Gm1m2(1130124)
=6.67*10^-11(3*10^-6)(10*10^-6)((24-130)/(24*130))=6.671011(3106)(10106)(2413024130)
=6.67*3*10*10^-23((-106)/(24*130))=6.673101023(10624130)
=-6.79*10^-23J=6.791023J