Question

Two objects have masses of `39 MG` and `18 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `81 m` to `3 m`?

Answer 1

The change in gravitational potential energy is `=1503*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=39MG=39*10^6g=39*10^3kg`

The mass is `M_2=18MG=18*10^6g=18*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=81m`

The distance `R_2=3m`

Therefore,

`Phi_1=(-G*(39*10^3*18*10^3)/81)`

`Phi_2=(-G*(39*10^3*18*10^3)/3)`

So,

`Phi_1-Phi_2=(-G*(39*10^3*18*10^3)/81)-(-G*(39*10^3*18*10^3)/3)`

`=39*18*10^6*6.67*10^-11(1/3-1/81)`

`=1503*10^-5J`