Two objects have masses of #39 MG# and #18 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #81 m# to #3 m#?

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Answer 1 · 2018-03-22T18:04:00

The change in gravitational potential energy is #=1503*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=39MG=39*10^6g=39*10^3kg#

The mass is #M_2=18MG=18*10^6g=18*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=81m#

The distance #R_2=3m#

Therefore,

#Phi_1=(-G*(39*10^3*18*10^3)/81)#

#Phi_2=(-G*(39*10^3*18*10^3)/3)#

So,

#Phi_1-Phi_2=(-G*(39*10^3*18*10^3)/81)-(-G*(39*10^3*18*10^3)/3)#

#=39*18*10^6*6.67*10^-11(1/3-1/81)#

#=1503*10^-5J#