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  • The acceleration due to gravity at the moon’s surface is 1.67 m s^{–2}. If the radius of the moon is 1.74 × 10^6 m, calculate the mass of the moon.

The acceleration due to gravity at the moon’s surface is 1.67 m s^{–2}. If the radius of the moon is 1.74 × 10^6 m, calculate the mass of the moon.

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\\As , g=\frac{G M}{R^{2}}$ or $M=\frac{g R^{2}}{G}$ \\ \\This relation is true not only to the earth but for any heavenly body which is assumed to be spherical Now, $g=1.67 m s^{-2}, R=1.74 \times 10^{6} m$ \\ \\$G=6.67 \times 10^{-11} Nm ^{-2} kg ^{-2}$ \\ \\ $\therefore$ Mass of the moon, $M=\frac{1.67 \times\left(1.74 \times 10^{6}\right)^{2}}{6.67 \times 10^{-11}} kg$ $=7.58 \times 10^{22} kg$

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Deependra Verma

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