Suppose the mass of the moon is M_{m} and its radius is R_{m}. If a body of mass *m *is placed on the surface of moon, then weight of the body on the moon is

*W*_{m }= {𝐺𝑀_𝑚𝑚 \over 𝑅_𝑚^{2}} … (1)

Weight of the same body on the earth’s surface will be

W_{e} = {𝐺𝑀_𝑒𝑚 \over 𝑅_𝑒^2} … (2)

where M, = mass of earth and R_{e }radius of earth.

Dividing equation (1) by (2), we get

{𝑊_𝑚 \over 𝑊_𝑒} = {𝑀_𝑚 \over 𝑀_𝑒} × {𝑅_𝑒^2 \over 𝑅_𝑚^2} … (3)Now, mass of the earth, *M** _{e} *= 6 x 10

^{24}kg

mass of the moon, *M*_{m }= 7.4 x 10^{22} kg

radius of the earth, R e = 6400 km

and radius of the moon, *R*_{m }= 1740 km

Thus, equation (3) becomes,

= {𝑊_𝑚 \over 𝑊_𝑒} = {7.4 ×10^{22}kg \over 6×10^{24}kg} × ({ 6400 km \over 1740 km}) ^{2}

Or, {𝑊_𝑚 \over W_ 𝑒} ≈ {1\over6}

Or, *W**m *≈ {𝑊_𝑒 \over 6}

The weight of the body on the moon is about one-sixth of its weight on the earth.