Question

Two objects have masses of `42 MG` and `25 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `48 m` to `15 m`?

Answer 1

The change in gravitational potential energy is `=321*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=42MG=42*10^6g=42*10^3kg`

The mass is `M_2=25MG=25*10^6g=25*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=48m`

The distance `R_2=15m`

Therefore,

`Phi_1=(-G*(42*10^3*25*10^3)/48)`

`Phi_2=(-G*(42*10^3*25*10^3)/15)`

So,

`Phi_1-Phi_2=(-G*(42*10^3*25*10^3)/48)-(-G*(42*10^3*25*10^3)/15)`

`=42*25*10^6*6.67*10^-11(1/15-1/48)`

`=321*10^-5J`