Two objects have masses of $9 M G$ $9 MG$ and $5 M G$ $5 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $24 m$ $24 m$ to $48 m$ $48 m$ ?

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Answer 1 · 2018-04-06T13:22:24

The gravitational energy will change by $= 0.9375 \cdot 10^{- 5} J$ $=0.9375*10^-5J$

Gravitational potential is the potential energy per kilogram at a point in a field.

So the units are $J, Joules$ $J, "Joules"$

$Phi=-G(M_1M_2)/R$

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 $M_1=9MG=9*10^6g=9*10^3kg$

The mass is $M_2=5MG=5*10^6g=5*10^3kg$

The distance between the centers is $=Rm$

The distance $R_1=24m$

The distance $R_2=48m$

Therefore,

$Phi_1=(-G*(9*10^3*5*10^3)/24)$

$Phi_2=(-G*(9*10^3*5*10^3)/48)$

So,

$Phi_1-Phi_2=(-G*(9*10^3*5*10^3)/24)-(-G*(9*10^3*5*10^3)/48)$

$=9*5*10^6*6.67*10^-11(1/48-1/24)$

$=-0.9375*10^-5J$

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