Two objects have masses of $4 MG$ and $8 MG$ . 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 · 2018-02-04T19:49:28

The change in potential energy is $=0.63*10^-5J$

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 $M_1=4MG=4*10^6g=4*10^3kg$

The mass is $M_2=8MG=8*10^6g=8*10^3kg$

The distance between the centers is $=Rm$

The distance $R_1=150m$

The distance $R_2=270m$

Therefore,

$Phi_1=(-G*(4*10^3*8*10^3)/150)$

$Phi_2=(-G*(4*10^3*8*10^3)/270)$

So,

$Phi_1-Phi_2=(-G*(4*10^3*8*10^3)/150)-(-G*(4*10^3*8*10^3)/270)$

$=4*8*10^6*6.67*10^-11(1/270-1/150)$

$=-0.63*10^-5J$

Two objects have masses of 4 MG4 MG and 8 MG8 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?