Two objects have masses of $3 MG$ and $15 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $130 m$ to $24 m$ ?

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Answer 1 · 2018-02-25T10:30:32

The change in gravitational potential energy is $=10.2*10^-5J$

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

The mass is $M_2=15MG=15*10^6g=15*10^3kg$

The distance between the centers is $=Rm$

The distance $R_1=130m$

The distance $R_2=24m$

Therefore,

$Phi_1=(-G*(3*10^3*15*10^3)/130)$

$Phi_2=(-G*(3*10^3*15*10^3)/24)$

So,

$Phi_1-Phi_2=(-G*(3*10^3*15*10^3)/130)-(-G*(3*10^3*15*10^3)/24)$

$=3*15*10^6*6.67*10^-11(1/24-1/130)$

$=10.2*10^-5J$

Two objects have masses of 3 MG3 MG and 15 MG15 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 130 m130 m to 24 m24 m?