Question

Two objects have masses of `5 MG` and `12 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `150 m` to `270 m`?

Answer 1

The change in gravitational potential energy is `=1.19*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=5MG=5*10^6g=5*10^3kg`

The mass is `M_2=12MG=12*10^6g=12*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=150m`

The distance `R_2=270m`

Therefore,

`Phi_1=(-G*(5*10^3*12*10^3)/150)`

`Phi_2=(-G*(5*10^3*12*10^3)/270)`

So,

`Phi_1-Phi_2=(-G*(5*10^3*12*10^3)/150)-(-G*(5*10^3*12*10^3)/270)`

`=5*12*10^6*6.67*10^-11(1/270-1/150)`

`=-1.19*10^-5J`