Question

Two objects have masses of `4 MG` and `18 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `7 m` to `2 m`?

Answer 1

The gravitational eneregy changes by `=4.81*10^-3J`

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=4MG=4*10^6g=4*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=7m`

The distance `R_2=2m`

Therefore,

`Phi_1=(-G*(4*10^3*18*10^3)/7)`

`Phi_2=(-G*(4*10^3*18*10^3)/2)`

So,

`Phi_1-Phi_2=(-G*(4*10^3*18*10^3)/7)-(-G*(4*10^3*18*10^3)/2)`

`=4*18*10^6*6.67*10^-11(1/2-1/7)`

`=480.6*10^-5J`