Question

Two objects have masses of `9 MG` and `5 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `24 m` to `48 m`?

Answer 1

The gravitational energy will change by `=0.9375*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=9MG=9*10^6g=9*10^3kg`

The mass is `M_2=5MG=5*10^6g=5*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=24m`

The distance `R_2=48m`

Therefore,

`Phi_1=(-G*(9*10^3*5*10^3)/24)`

`Phi_2=(-G*(9*10^3*5*10^3)/48)`

So,

`Phi_1-Phi_2=(-G*(9*10^3*5*10^3)/24)-(-G*(9*10^3*5*10^3)/48)`

`=9*5*10^6*6.67*10^-11(1/48-1/24)`

`=-0.9375*10^-5J`