the distance between center of Earth and center of Moon isconsidered to be R. So

Question

the distance between center of Earth and center of Moon isconsidered to be R. Somewhere between the Earth and the Moon is a point where thegravitational attraction of the Earth is canceled by thegravitational pull of the Moon. The mass of the Moon is 1/81 that of the Earth. How far from the center of the Earth (in terms of R) is thispoint????? the distance between center of Earth and center of Moon isconsidered to be R. Somewhere between the Earth and the Moon is a point where thegravitational attraction of the Earth is canceled by thegravitational pull of the Moon. The mass of the Moon is 1/81 that of the Earth. How far from the center of the Earth (in terms of R) is thispoint?????

Explanation / Answer

let D be the distence between theearth and moon centres

let R and r be the distances to thepoint where force of gravity due to earth and mooncancels

            earthforce   Fe = GMem / R^2  

                and for moon Fm = GMm . m /(D-R)^2

       

                      Fe = Fm

             Me / R^2 = Mm / (D-R)^2.given Me = 81Mm

      frm thisrelation we can sovle for R .

                   81(D-R)^2= R^2

                                                       

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