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 $270 m$ ?

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Answer 1 · 2018-03-03T14:41:34

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

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 $M_1=5MG=5*10^6g=5*10^3kg$

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,

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

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

$=-1.19*10^-5J$

Two objects have masses of 5 MG5 MG and 12 MG12 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 150 m150 m to 270 m270 m?