Question

The distance between the moon and earth is `3.8 xx 10^(8)m`. Find the gravitional potential at the mid point of the joining them. Given that the mass of the earth is `6 xx 10^(24) kg`, mass of moon `= 7.4 xx 10^(22) kg` and `G = 6.67 xx 10^(11) Nm^(2)kg^(-2)`.

Answer 1

Here `M_(e) = 6 xx 10^(24) kg, M_(m) = 7.4 xx 10^(22) kg, r = 3.8 xx 10^(8) m`
Gravitational potential due to the earth at the mid point `O` of the line earth and moon is
`V_(1) = (-GM_(e))/((r//2)) = (-2GM_(e))/(r )`
Gravitational potential due to the moon at the mid point `O` of the joining the earth and moon is
`V_(2) = (-GM_(m))/((r//2)) = (-2GM_(m))/(r )`
Total gravitational potential at `O` is
`V = V_(1) + V_(2) = (-2G)/(r ) [M_(e) + M_(m)]`
`= (-2 xx (6.67 xx 10^(-11)))/(3.8 xx 10^(8)) [6 xx 10^(24) + 7.4 xx 10^(22)]`
`= - 2.13 xx 10^(6) J kg ^(-1)`