Question

Two objects have masses of `22 MG` and `23 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `25 m` to `75 m`?

Answer 1

The change in gravitational potential energy is `=90*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=22MG=22*10^6g=22*10^3kg`

The mass is `M_2=23MG=23*10^6g=23*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=25m`

The distance `R_2=75m`

Therefore,

`Phi_1=(-G*(22*10^3*23*10^3)/25)`

`Phi_2=(-G*(22*10^3*23*10^3)/75)`

So,

`Phi_1-Phi_2=(-G*(22*10^3*23*10^3)/25)-(-G*(22*10^3*23*10^3)/75)`

`=22*23*10^6*6.67*10^-11(1/75-1/25)`

`=-90*10^-5J`