Question

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`?

Answer 1

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

Explanation:

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`