The distance between earth and moon is `3.8 xx 10^(8)m`. Determine the gravitational potential energy of earth-moon system. Given, mass of the earth `= 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)`

Explanation

Here, `m = 250 g = 0.250 kg`,
`M = 5.983 xx 10^(24) kg, R = 6.378 xx 10^(6) m`
Gravitational force between mango and Earth
is `F = (GMm)/(R^(2))`
Acceleration of the mango towards the Earth
`a = (F)/(m) = (GM)/(R^(2))`
`= ((6.67 xx 10^(-11))xx(5.983 xx 10^(24)))/((6.378 xx 10^(6))^(2))`
`= 9.81 ms^(-2)`
Acceleration of Earth towards the mango
`a' = (F)/(M) = (Gm)/(R^(2)) = ((6.67 xx 10^(-11))xx(0.25))/((6.378 xx 10^(6))^(2))`
`= 4.1 xx 10^(-25) ms^(2)`