Two objects have masses of $42 M G$ $42 MG$ and $25 M G$ $25 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $21 m$ $21 m$ to $15 m$ $15 m$ ?

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Answer 1 · 2018-04-04T14:46:50

The change in gravitational energy is $= 133.4 \cdot 10^{- 5} J$ $=133.4*10^-5J$

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 $M_1=42MG=42*10^6g=42*10^3kg$

The mass is $M_2=25MG=25*10^6g=25*10^3kg$

The distance between the centers is $=Rm$

The distance $R_1=21m$

The distance $R_2=15m$

Therefore,

$Phi_1=(-G*(42*10^3*25*10^3)/21)$

$Phi_2=(-G*(42*10^3*25*10^3)/15)$

So,

$Phi_1-Phi_2=(-G*(42*10^3*25*10^3)/21)-(-G*(42*10^3*25*10^3)/15)$

$=42*25*10^6*6.67*10^-11(1/15-1/21)$

$=133.4*10^-5J$

Two objects have masses of 42 MG42MG42 MG and 25 MG25MG25 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 21 m21m21 m to 15 m15m15 m?