Two objects have masses of #5 MG# and #12 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #150 m# to #270 m#?

1 Answer
Mar 3, 2018

The change in gravitational potential energy is #=1.19*10^-5J#

Explanation:

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=5MG=5*10^6g=5*10^3kg#

The mass is #M_2=12MG=12*10^6g=12*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=150m#

The distance #R_2=270m#

Therefore,

#Phi_1=(-G*(5*10^3*12*10^3)/150)#

#Phi_2=(-G*(5*10^3*12*10^3)/270)#

So,

#Phi_1-Phi_2=(-G*(5*10^3*12*10^3)/150)-(-G*(5*10^3*12*10^3)/270)#

#=5*12*10^6*6.67*10^-11(1/270-1/150)#

#=-1.19*10^-5J#