Two objects have masses of #22 MG# and #23 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #25 m# to #75 m#?

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Answer 1 · 2018-03-03T09:06:08

The change in gravitational potential energy is #=90*10^-5J#

Gravitational potential is the potential energy per kilogram at a point in a field.

So the units are #J, "Joules"#

#Phi=-G(M_1M_2)/R#

The gravitational universal constant is

#G=6.67*10^-11Nm^2kg^-2#

The masses causing the field is #=M_1 kg# and #=M_2 kg#

The mass is #M_1=22MG=22*10^6g=22*10^3kg#

The mass is #M_2=23MG=23*10^6g=23*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=25m#

The distance #R_2=75m#

Therefore,

#Phi_1=(-G*(22*10^3*23*10^3)/25)#

#Phi_2=(-G*(22*10^3*23*10^3)/75)#

So,

#Phi_1-Phi_2=(-G*(22*10^3*23*10^3)/25)-(-G*(22*10^3*23*10^3)/75)#

#=22*23*10^6*6.67*10^-11(1/75-1/25)#

#=-90*10^-5J#