Question

Two objects have masses of `4 MG` and `26 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `7 m` to `9 m`?

Answer 1

The change in gravitational potential energy is `=-22.02*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=4MG=4*10^6g=4*10^3kg`

The mass is `M_2=26MG=26*10^6g=26*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=7m`

The distance `R_2=9m`

Therefore,

`Phi_1=(-G*(4*10^3*26*10^3)/7)`

`Phi_2=(-G*(4*10^3*26*10^3)/9)`

So,

`Phi_1-Phi_2=(-G*(4*10^3*26*10^3)/7)-(-G*(4*10^3*26*10^3)/9)`

`=4*26*10^6*6.67*10^-11(1/9-1/7)`

`=-22.02*10^-5J`